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Rationalisation | Rationalisation Exercise 3.2

Question 1

: Rationalise the denominators of each of the following (i – vii): (i) 3/ √5

(ii) 3/(2 √5)

(iii) 1/ √12

(iv)√2/ √5

(v) (√3 + 1)/ √2

(vi) (√2 + √5)/ √3

(vii) 3 √2/ √5

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  • Solution

  • Transcript

"hello students welcome to lido homework i'm tutor arguswati from lido learning now let us rationalize the denominators of each of the following expressions so rationalizing the denominator means there should not be any irrational number in the denominator so let us take our first question and rationalize it the first is 3 by root 5 see we are having a irrational number at the denominator it shouldn't be there so what we will do is that we will take this irrational number and multiply it in the numerator as well as the denominator so 3 by root 5 into root 5 by root 5. so what we are doing we are multiplying root y with numerator and denominator so now our expression becomes 3 into root 5 is 3 root 5 divided by root 5 into root 5 is 5. now we got our rationalized form therefore the rationalized form of 3 by root 5 is equal to 3 root 5 divided by 5. now let us go to our second question 3 divided by 2 root 5 here also we have root 5 as our irrational number so we will take that root 5 and multiply it with the numerator as well as the denominator so now it becomes 3 root 5 divided by 2 is only 2 and root 5 into root 5 is 5 therefore we will get it as 3 root 5 by 10. therefore the rationalized denominator of the question 3 by 2 root 5 is equal to 3 root 5 by 10. now we'll go for our third question which is 1 by root 12 so root 12 is an irrational number so that we'll take it and multiply it with numerator as well as the denominator so root 12 divided by root 12 which is root 12 divided by 12. therefore the rationalized form will be root 12 divided by 12. but here we could write 12 as 4 into 3 and similarly 12 can also be written as 3 into 4 so we know that root 4 is 2 so we'll get 2 root 3 by 3 into 4 so 4 and 2 gets cancelled so that we'll get root 3 by 3 into 6 that is 6. so the answer is root 3 by 6 therefore the rationalized form of 1 divided by root 12 is equal to root 3 by 6. now let us go for our fourth question which is root 2 by root 5 so root 5 is our irrational number so that we'll take this root 5 and multiply it with denominator as well as the numerator root 2 into root 5 is root 10 and root 5 into root 5 is 5 therefore the rationalized denominator of root 2 by root 5 is equal to root 10 by 5 or we could also write this as 1 by 5 into root 10 now we will go to our fifth question which is root 3 plus 1 divided by root 2. so root 2 is our irrational number so we'll take this term and multiply so it becomes true 3 plus 1 by root 2 into root 2 divided by root 2. so this root is common for both the things so we could write root 3 into root 2 will be root 6 and 1 into root 2 is root 2 plus root 2 and root 2 into root 2 will be 2 therefore the rationalized denominator of the term root 2 by root 5 is equal to root 6 plus root 2 divided by 2. now we'll solve our sixth question which is root 2 plus root 5 divided by root 3 so root 3 is our irrational number here so that root 3 will be multiplied with the numerator as well as the denominator so root 2 plus root 5 divided by root 3 into root 3 divided by root 3 so root 2 into root 3 is root 6 plus root 5 into root 3 is root 15 and in the denominator root 3 into root 3 is 3 therefore the rationalized denominator of the expression root 2 plus root 5 divided by root 3 is equal to root 6 plus root 15 divided by 3 now we'll solve our last one which is 3 root 2 divided by root 5 here root y is the irrational number so that will take root 5 and multiply it with the numerator and the denominator so that it becomes 3 root 2 divided by root 5 into root 5 divided by root 5. so we will get 3 and root 2 into root 5 is root 10 divided by 5 because root 5 into 5 is 5 therefore the rationalized denominator of the expression 3 root 2 divided by root 5 is equal to 3 root 10 divided by 5. if you have any doubts please post your questions in the comment box and subscribe the channel for regular updates thank you "

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Question 1

: Rationalise the denominators of each of the following (i – vii): (i) 3/ √5

(ii) 3/(2 √5)

(iii) 1/ √12

(iv)√2/ √5

(v) (√3 + 1)/ √2

(vi) (√2 + √5)/ √3

(vii) 3 √2/ √5

  • Solution

  • Transcript

"hello students welcome to lido homework i'm tutor arguswati from lido learning now let us rationalize the denominators of each of the following expressions so rationalizing the denominator means there should not be any irrational number in the denominator so let us take our first question and rationalize it the first is 3 by root 5 see we are having a irrational number at the denominator it shouldn't be there so what we will do is that we will take this irrational number and multiply it in the numerator as well as the denominator so 3 by root 5 into root 5 by root 5. so what we are doing we are multiplying root y with numerator and denominator so now our expression becomes 3 into root 5 is 3 root 5 divided by root 5 into root 5 is 5. now we got our rationalized form therefore the rationalized form of 3 by root 5 is equal to 3 root 5 divided by 5. now let us go to our second question 3 divided by 2 root 5 here also we have root 5 as our irrational number so we will take that root 5 and multiply it with the numerator as well as the denominator so now it becomes 3 root 5 divided by 2 is only 2 and root 5 into root 5 is 5 therefore we will get it as 3 root 5 by 10. therefore the rationalized denominator of the question 3 by 2 root 5 is equal to 3 root 5 by 10. now we'll go for our third question which is 1 by root 12 so root 12 is an irrational number so that we'll take it and multiply it with numerator as well as the denominator so root 12 divided by root 12 which is root 12 divided by 12. therefore the rationalized form will be root 12 divided by 12. but here we could write 12 as 4 into 3 and similarly 12 can also be written as 3 into 4 so we know that root 4 is 2 so we'll get 2 root 3 by 3 into 4 so 4 and 2 gets cancelled so that we'll get root 3 by 3 into 6 that is 6. so the answer is root 3 by 6 therefore the rationalized form of 1 divided by root 12 is equal to root 3 by 6. now let us go for our fourth question which is root 2 by root 5 so root 5 is our irrational number so that we'll take this root 5 and multiply it with denominator as well as the numerator root 2 into root 5 is root 10 and root 5 into root 5 is 5 therefore the rationalized denominator of root 2 by root 5 is equal to root 10 by 5 or we could also write this as 1 by 5 into root 10 now we will go to our fifth question which is root 3 plus 1 divided by root 2. so root 2 is our irrational number so we'll take this term and multiply so it becomes true 3 plus 1 by root 2 into root 2 divided by root 2. so this root is common for both the things so we could write root 3 into root 2 will be root 6 and 1 into root 2 is root 2 plus root 2 and root 2 into root 2 will be 2 therefore the rationalized denominator of the term root 2 by root 5 is equal to root 6 plus root 2 divided by 2. now we'll solve our sixth question which is root 2 plus root 5 divided by root 3 so root 3 is our irrational number here so that root 3 will be multiplied with the numerator as well as the denominator so root 2 plus root 5 divided by root 3 into root 3 divided by root 3 so root 2 into root 3 is root 6 plus root 5 into root 3 is root 15 and in the denominator root 3 into root 3 is 3 therefore the rationalized denominator of the expression root 2 plus root 5 divided by root 3 is equal to root 6 plus root 15 divided by 3 now we'll solve our last one which is 3 root 2 divided by root 5 here root y is the irrational number so that will take root 5 and multiply it with the numerator and the denominator so that it becomes 3 root 2 divided by root 5 into root 5 divided by root 5. so we will get 3 and root 2 into root 5 is root 10 divided by 5 because root 5 into 5 is 5 therefore the rationalized denominator of the expression 3 root 2 divided by root 5 is equal to 3 root 10 divided by 5. if you have any doubts please post your questions in the comment box and subscribe the channel for regular updates thank you "

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