[Music] good day everyone in this video lesson we will discuss about simplifying radical expression our objective is to simplify radical expression using the laws of radicals okay but first class uh a perfect square so a guy named square root of eight so petty panting is simplified as a an eight i may factor in a perfect squared you know four no so by simplifying a square root of eight so petty nothing and going two square root of two okay my number nahindi sila perfect so you square that of 12 that is 2 square root of 3 square root of 18 that is 3 square root of 2 square root of 20 that is 2 square root of 5 square root of 24 2 square root of 6 square root of 27 that is 3 square root of 3 square root of 28 that is 2 square root of 7 square root of 32 that is 4 square root of 2 square root of 40 that is 2 square root of 10 square root of 44 that is 2 square root of 11 square root of 45 that is 3 square root of 5 square root of 48 that is 4 square root of 3 square root of 50 that is 5 square root of 2 square root of 52 that is 2 square root of 13 square root of 54 that is 3 square root of 6 square root of 56 that is 2 square root of 14 square root of 6 t that is 2 square root of 15 square root of 63 that is 3 square root of 7 square root of 68 that is 2 square root of 17 square root of 72 that is a 6 square root of 2. square root of 75 that is 5 square root of 3 square root of 76 that is 2 square root of 19 square root of 80 that is 2 square root of 7 or that is 4 square root of 7 ladder again square root of eighty that is four square root of seven square root of eighty four that is four square root of two uh-huh that's 84 so that should be okay for square root of 84 that is 2 square root of 21 square root of 88 that is 4 square root of 2 or 2 square root of 22 square root of 19 that is 3 square root of 10 square root of 92 that is 2 square root of 33 at 2 square root of 23 ladder square root of 96 that is 4 square root of 6 square root of 98 that is 7 square root of 2 and square root of 99 that is three square root of eleven so it in first one hundred name factor in a perfect squared so that pattern familiarize things perfect square young events simplify okay but simplifying radical expression e big sub nearly removed nothing on perfect n power so for example we have the square root of the product of two non-negative numbers is equal to the product of their square roots okay for example we have the square root of eight x to the fifth power white the six z to the thirteenth power so i'm gonna go in that in classes so express perfect square that is four times two so um classic x to the fifth and z to the thirteen so uh i'm gonna go in that and express nothing is some factor i predict in my dividends expressed as four times two casing i am for i may is perfect squared so petty not into marijuana radical radicand nothing since your index nothing is too so hindu number nothing pretty much the volume five divide two so i'm getting nothing to nothing no law of uh exponent number number multiply nothing that's x to the fifth so x to the fourth times x okay so again so it don't for 13 so z raised to 12 or z to the 12th power times a so equal paring and it is a to the 13th power you say to the twelve pretty not indian removed index so now since marie removed not in c4 radical radicands so square root of four that is two so my e1 getting into salute okay x to the fourth so it'll divide like nothing square root so four divide two so that is two yeah la la bassy x squared my e one say x and o y to the sixth so c six multi divide not insert z to the 12th power so 12 divide two camera uh that is z to the six so my e1cc so therefore the final answer is two x squared y cubed z to the sixth power square root of two x z okay so genius is simplified in a radical expression it perfect and powers next european in reduce the index to the lowest possible order for example the m fruit of the end root of a or that is the product of young index not in the m n of a times the n root of m root of a okay so halimbawa melon 20 root of 32 m to the 15 and to the fifth power so nothing class divided 20 sub 5 so i'm going to really do some index [Music] okay since i'm 32a that is equivalent to 2 to the fifth power and then m 15 m to the 15th power so pedi nothing in legend uh and then raised to one over twenty can say twenty index nathan and then it all ready nothing in multiply now applying the uh this is the law of exponentia power by power yeah no power of a power so that is 5 times 1 over 20 that is 2 raised to 1 4 15 times 1 over 20 that is 3 4 okay 5 times 1 over 20 that is one percent same dimension and denominator so betty nothing going in 2 m cube and n raised to one fourth uh doing some more previous video lesson attend uh discuss not comparing nothing from exponential to radical discussion in so young max is served as index not answer that is fourth root of two m cube n okay i'll give you more example so simplify its radical first the square root of x to the fifth okay and the tone to class so nothing since undergoing an attend pagnexy simplified in radical expression uh it really does not end so pretty nothing expresses x to the fourth x that is x to the fifth exit the fourth and so the square root of x to the fourth times square root of x so in square root of x to the fourth i bet in that and it divides the index that is 4 divided so that is x squared square root of x okay so nothing you may perfect uh squared and then you hindi removes next cube root of b to the seventh power okay young index not indeed i three so since c7 and nothing dividing that is a number one so petting that expression b to the seventh power asset uh b raised to six times b okay divided index not n so therefore uh cube root of b to the sixth power times cube root of b so it almost divide that and so six divide to that is b squared cube root of b okay next a square root of 63 m squared okay sees c63 a metal factor in a perfect square it is a perfect square but my factors a perfect squared and that is nine times seven times m squared so uh perfect square tama nothing expression nama remove nothing so square root of 9 that is 3 square root of m squared divided by 2 divided so m square root of 7. another example we have square root of 60 x to the fourth y to the fifth power so 60 and this is a perfect squared factors in my firefox squared and that is 15 times four so young four is a perfect squared so nothing is so is 15 y okay so therefore square root of four that is two square root of x to the fourth somebody divide that and that's x squared square root of y to the fourth that is y squared square root of 15y okay that will be the final answer another we have 45 x cubed as square root of 45 x cubed y to the eighth power okay so i'm 45 we can express as nine times five and then say x cubed since index not in d to a two super d not in a expressed number x cube i x squared times x see why to the eighth power since even nothing dividing so and then pakistan not impeding my remove see nine c x squared at c white at the eighth power so therefore the square root of nine is three square root of x squared that is x squared of y to the eighth powers y to the fourth okay and then square root of five x another example we have the cube root of 125 x to the fifth y to the 18th power okay so see 125 by perfect cube yes it's a a perfect cube yeah because 5 billion in perfect um cube root 125 is five tama okay so 100 cube root of 125 times x cubed times x squared times y to the 18th power so pin accurately nothing x to the fifth so you three and two so therefore after that uh perfect cube radicand so it so therefore the cube root of 125 that is five cube root of x cubed that is x because it three divided three that's x 18 divided three that is six k y to the sixth power and cube root of x squared next we have 56 a cube root of 56 m to the tenth and to the 12th so see 56 spreading that in express as eight times seven kcc eight is a perfect cube no a young factor in eight is a perfect cube and that is two and then ten since three young index net and super express latin is m raised to nine times m policy nine ma tango nothing somebody divide nothing in c3 so enter the twelves so i'm going to say oh by you seven second m so that is the cube root of seven m in cube root n eighth not and that is two uh m to the ninth power that is m cube and then twelve divided that's enter the fourth cube root of x squared next number eight cube root of negative sixteen x to the sixth y cubes eight two to the twelfth power nameless negative petty and mccarran tiny negative sign okay so see negative 16 perfect um factoring so where the young eight negative eight times two you say negative eight times two that is sixteen that's in negative eight i mean uh that is a melon shot it's a perfect cube in negative eight so and then you extend the sixth okay so cube root of negative eight that is negative two cube root of x to the sixth so six divided by that is x squared y cubed okay that is y in the lungs twelve divide three that is a to the fourth cube root of two another example we have negative forty x to the nine y to the tenth power so unknown perfect cube nope nothing give me ten okay negative 40 yes negative eight times five c9 y raised to ten because this is nothing but the divided three so so y to the ninth power times y okay and then pakistan nothing you're gonna go on that then so that is negative cube root of negative eight that is negative two at nine divide three that's x 9 divided by that is y cube and that is cube root of 5 y okay i hope that's also in discussion nothing okay so fourth root of 16 young index nothing is four so mel uh i'm 16 buys a perfect uh fourth route okay so c16 i aniano that is two times two times two times two two times two is four times to eight times to sixteen so anusha so that is 16 times x to the 12th hour times y to the 20 times y so therefore fourth root of 16 that is 2 12 divide four that is x cube 20 divide four that is y to the f power fourth root of y another example 81 so say 81 so nothing fourth routine 81 so 81 that is okay c3 okay times three nine times three twenty seven times three eighty one so in fourth routine eighty one is three so and then um that indication twenty five seven thirty seven so twenty four zero fourth root of 81 that is three 24 divided four that is six k p to the sixth power thirty six divided four that is nine so q to the ninth power fourth root of uh pq so another we have number 12 so negative 2x uh square root of 3xy cubes a to the seventh power so many times negative 2x syllabus so i'm going to then go in [Music] so therefore uh negative 2x uh square root of y squared z to the sixth times the square root of three x y z so it is uh perfect and anonymous squared so petty not in marimubian so square root of y squared that is y z to the sixth power that is six divide two that is three and then multiply not initially negative two x okay so negative two x times yz cubed the answer is negative 2xyz cubed square root of 3xyz next we have square root of 3 raised to 3 and 6 cubed or square root of three cubed times six cube since an index not n is two so patting a particularly nut into class okay so three squared times three times six squared times six the bar okay so not in so matatangal so three times six okay that is eighteen square root of eighteen is the square root of eighteen pretty but not into a simplified class so pano so it's the square root of 18 peripherality must simplify as 9 times 2 no square root of 9 times 2. so see 9 a square root of 9 that is 3 so a la la base not n so that is 18 times 3 square root of 2 so the answer is 54 square root of two next cube root of two to the fourth power and five to the fifth power so nothing since your index not indeed three so page so two cube times two times five cube times five squared so pakistan nothing yuma remove nothing so it'll remove nothing so that is two times five and that is cube root of 2 times 25 so therefore the answer is 10 cube root of 50. last example we have 5 x to the fourth y squared square root of 4 over 25 x to the 20th power y to the 30. since you uh index nothing is 2 at young 4 25 is perfect squared such as 20 and 30 by the nothing it divides okay so that is 5 x to the fourth y squared times square root of 4 is 2 square root of 25 is 5 get 2 fifth x 20 divided that's x to the 10 15 divided that is y to the 15th power so the answer is support me multiply nothing five times two trips to my cancellation the base omega two x to the fourth times x to the ten so that is x to the fourteen y to the y squared times y to the 15th power that is y to the 17th power okay so that's all so i hope nassundang in discussion how to simplify a radical expression thank you for watching this video i hope you learned something don't forget to like subscribe and hit the bell button put updated ko for more video tutorial 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