[Music] in this video we will familiarize ourselves with the numbers that are perfect squares and we will solve quadratic equations by extracting square roots so first that are perfect squares so like 1 4 9 16 25 36 and so on and so forth numbers no perfect squares at hindi perfect square so quadratic equations by extracting the square roots all right how to extract square roots okay since our given is a perfect square we all know that 49 is a perfect square so major medallion square all right so first get the square root of both sides so we will have square root of x squared is equal to positive or negative square root of 49 so next step get the square root of x squared so we have x and square root of 49 that will become 7 so therefore our solution is x is equal to positive or negative 7. next again 169 is a perfect square so again first step get the square root of both sides so we will have square root of x squared is equal to positive or negative square root of 169 so we will now have the square root of x squared which is x and then the square root of 169 which is 13 so the solutions are x is equal to positive or negative 13. now what if the given is not a perfect square number [Music] hindi perfect square okay let's have an example so i'm giving you a table parameter so x squared is equal to 75 75 is not a perfect square okay so first get the square root of both sides go not in your square root on both sides so we will have square root of x squared is equal to square root of seventy five so i know among the factors is seventy five now and perfect square so puede nothing if after it all gamete 25 times 3 because 25 is a perfect square right so we will now have x is equal to positive or negative square root of 25 times 3 okay 25 times 3 perfect square c 75 now let us now get the square root of the perfect square so number in a perfect square so we will have x is equal to positive or negative square root of 25 times square root of three alumni 25 i perfect square so we will have x is equal to positive or negative five square root of three so naivan parensis three cases not a perfect square next x squared is equal to 80 so again 80 is not a perfect square so get the square root of both sides we have square root of x squared is equal to square root of 80. so let us now find the factors of 80 named perfect squares so again we have 16 times 5 16 if is a perfect square so x is equal to positive or negative square root of 16 times 5 so get the square root of the perfect square since 16 i perfect square so x is equal to positive or negative square root of 16 times square root of five 16 is a perfect square so extract nothing on we will have x is equal to positive or negative four square root of five so c five nandunparin shah has a five is not a perfect square okay what if you were given this kind of example example so i have here 2 times the quantity of x minus 5 raised to 2 is equal to 32 so first we have to divide both sides by two so you divide not in both sides by two para cancel not in c two so we will now have x minus five raised to 2 or the quantity of x minus 5 raised to 2 is equal to 16 bucket again 16 2 so 32 divide 2 that is 16 next get the square root of both sides so we will now have the square root of the square of the quantity of x minus five is equal to square root of sixteen so we will now have x minus five is equal to positive or negative 4. so since 4 may be positive or negative therefore we will have two equations okay so since [Music] positive or negative four since poison positive though or negative therefore makaharan and equations so the first equation is x minus five is equal to four so we will solve for x so that will become x is equal to four plus five therefore x is equal to nine this is our first root or solution and then the second equation is x minus five is equal to negative four so x is equal to negative four plus five so we will have x is equal to one so the roots or solution of the given quadratic equation is nine and one next i have here three times the quantity of four x minus one squared minus one is equal to eleven so since meron tayo minus one dito ilipatnam so that will become three times the quantity of four x minus one squared is equal to twelve so eleven plus one again twelve taiyo so since merunta young three parameters three divide both sides by what's left is for x minus one squared is equal to four bahitnegan so 12 divided three is equal to four so get the square root of both sides so we will now have the square root of the square of quantity four x minus one is equal to the square root of four so we will have four x minus one is equal to positive or negative two so again since positive and negative so the first equation is 4x minus 1 is equal to 2 at 4x minus 1 is equal to negative 2 so lagging and on so let's ask solve first the first equation for x minus 1 is equal to 2 so we have 4 x is equal to 3 y 3 because 2 lily but not in c 1 that will become positive so two plus one is equal to three next divide both sides by four so magazines four density x and then we will have three fourths and then for our second equation we have four x minus one is equal to negative two so gonna let for x is equal to negative one backhand because a negative two eliminates a negative one so negative two plus one again negative one so divide both sides by four so we will now have x is equal to negative one fourths next i have here the quantity of 2x minus 3 squared is equal to 18. so get the square root of both sides we have so since walana mantayung numbers outside the parenthesis so we will now have square root of 2x minus 3 squared is equal to square root of eighteen so young 18 is not a perfect square so hanaptayo nonfactors perfect square kai 18 so we have now 9 times two see nine a perfect square so magicking two x minus three is equal to positive or negative square root of nine times square root of two since against in c9 i perfect square puedena illa bass magicking 2x minus 3 is equal to positive or negative 3 square root of 2. ulit inco since positive but negative ito e big sub 1 equations not in veto so we will have 2x minus 3 is equal to 3 square root of 2 you are not in a positive so 2x is equal to three elite but nothing's a negative three plus capital new lungs is three square root of two and then we will have now x is equal to three plus three square root of two over two so by negan x both sides by two on our second equation we have two x minus three is equal to negative numanito negative 3 square root of 2 so 2x is equal to 3 li but nothing say negative 3 minus 3 square root of 2. so x is equal to 3 minus 3 square root of 2 over 2 so again divide lag nut and both sides by 2. okay i have here 2 times the quantity of 5x plus 2 squared is equal to 64. so first step divide both sides by two since meron tayanto dito so para cancel nothing say so we now have 5x plus 2 squared or the quantity of 5x plus 2 squared is equal to 32 because 64 divided by 2. since now divide diode both sides by 2. so naging 32 nalang and then get the square root of both sides so we now have the square root of the square of quantity 5 x plus 2 is equal to the square root of 32 so we now have uh get the factors of 32 num perfect square so since 16 times 2 is equal to 32 and 16 is a perfect square so so we now have five x plus two is equal to positive or negative square root of sixteen times square root of two so cnc sixteen i perfect square by the national x plus two is equal to positive or negative four square root of two so since positive but negative shy big so we have the first equation 5x plus 2 is equal to positive 4 square root of 2 solve for x so we will have five x is equal to negative two the but nothing is positive two and then plus four square root of two so divide both sides by five so we will now have x is equal to negative two plus four square root of two over five on the other side our second equation negative naman so five x plus two is equal to negative positive lagging on positive and negative negative 4 square root of 2. solve for x we have 5x is equal to negative 2d but nothing is positive 2 that will become negative two and then negative a minus four square root of two so divide both sides by five we will come up with x is equal to negative two minus four square root of two over five thank you for watching this video i hope you learned something don't forget to like subscribe and hit the bell button to our walmart channel just keep on watching