foreign [Music] [Music] school inshallah I'm going to explain mathematics for grade nine in English language the first subject that you have in chapter one section one is square root before we talk about square roots there's an important definition you have to know and that is perfect square so what is perfect score perfect square is a number that can be expressed as a an integer by SL for example five okay times five okay multiplied by slf is equal 25 then we can say that 25 is perfect square or we have another definition it says as the what as the second exponent of an integer five times five you can write it as 5 squared is equal 25. so 25 is perfect square or let's say 4 times 4 is equal 16. then 60 is perfect square or 100 let's say 10 times 10 is equal 100 the 100 is a perfect square this is about perfect square then we have a list of some of the perfect squares 1 4 9 16 25 36 49 and so on this is the list of some of the perfect squares we have to know them because we will need them then you should know that one it comes from one times one four is comes from two times two three and nine is three times three and so on for the rest of the numbers then when you want to find the square root of perfect square it's quite easy for example if you want to find the square root of 4 it's going to be it's going to be 2. it's going to be two or you want to find the square of 49 it's going to be seven the score of 121 is equal 11. the square of 169 is equal 30. so finding the score of perfect square it is easy but sometimes you have non-perfect squares for example the score of 13 or the score of a the score of let's say 10 the score of 105 okay these numbers are not perfect square then how can we find the square of let's say 13 and the rest of the non-pepa squares okay to find the score of non-perfect squares we need perfect squares that's why I told you they are important you have to know them we need them okay let's uh solve some examples the first one it says find the square root of 20. the skirt off 20. as you know 20 is not perfect square because we cannot write or Express 20 as the product of a number by itself so how can you find the score of 20 let's write the perfect squares list 1 times 1 is 1 then 4 9 16. 25 36 okay then we have to find two perfect squares that 20 locates between them if I choose for example if I choose one and four can we say 20 is located between 1 and 4 or can you say 20 is located between 4 and 9 of course not we cannot say that so 20 is located between 16 at 25. 20 locates between 16 and 25 so 20 locates between 16 [Music] and 25 you know that the square root of 16 is for the score of 5 25 is 5 that's why the square of 20 locates between 4 and 5. okay let's complete the list 36 then you have 49 then you have 64. 81 100 121 140 for 169 196 225 and so on example B it says find the square root of 110 the square root of 110. okay then we are going to find two perfect square that 110 is located between then then let's check the numbers 110 is not here it's not here so it is there between 100 and 121 locates between 100 and 121 the score of 100 is 10. and the score of 121 is 11 so the score of 110 is locates between 10 and 11. 10 and 11. sometimes in the example or the question we have negative with the F square root the negative is outside it's not inside if you have let's say the square of negative 50 that is 95 we cannot solve it but but the negative is outside so how to solve it please do not care about the negative just focus on the number focus on the number 15. so we have one 4 9 16 25 then 15 is located between 9 and 16. 9 and 60. a scale of 15 write down the negative and locates between 25 and also 16. and then we are going to write the negative okay the score of 16 is 4 underscore of 25 is five negative square root of 15. so the negative score of 15 look is between negative 4 and negative 5. then we have some initial money questions it says which is square root lies between 11 and 12. maybe you focus on the answers first but do not focus on the answers directly we are going to square both number 11 times 11 is equal 121 12 times 12 is equal to 144. then which number lookates between 121 and 140 4. so if you say 100 let's say 2 102 is let's say located is far less 150 is greater also 170 is greater the only number is the answer is 131 so 131 is located between 11 and 12. question two uh 44 is located between two integers so we have 5 times 535 3 is 6 times 6 36 so 44 does not locate between 25 and 36. then we have 6 times 6 36 7 times 7 is 49 so 44 is located between 36 and 49 that's why it is 6 and so is the correct answer for C and D 7 times 749 a times a64 44 is not here for d as well 64 and 81 44 is not located between them that's why the correct answer is B question 3 which value is located between negative 7 and negative 8. again we are going to square both numbers 7 times 7 is 49. 8 times 8 is 64. so which number is located between 49 and 64. 65 is greater than 64 is let's say above them then 57 the correct answer is 57 57 look is between negative 49 and negative 64 that's why it's between negative 7 and negative 8. C is negative let's say 47 is less than 49 that's why I did not choose it and also this one's not the correct answer question four which two integers lie it does which two integers the 72 lie between so here 49 64. 25 36 36 49 81 and sorry 64. 64 and 81 so 72 is located between 64 and 81. D is the correct answer the last question which square root lies between 14 and 15. 14 times 14 6. 15 times 15 225 so which number lies between 196 and 225 so it is 200 200 locates between 196 and 225 okay dear lovely students this is the end of our class I hope you get benefits from me thanks for watching [Music] thank you