Rationalizing the Denominator Solution4






In this page rationalizing the denominator solution4 we are going to see solution of each questions of the worksheet rationalizing the denominator.We have explained each problems with step by step explanation.

Question 3

Rationalize the denominator (1 + 2√3)/(2 - √3) = x + y √3 and find the value of x and y.

Solution

L.H.S

In this question we have 1 + 2√3  in the numerator and 2 - √3 in the denominator so we have to multiply by its conjugate that is 2 + √3  with both numerator and denominator. Now the denominator is like in the form (a+ b) (a-b). So we have simplified this using a² - b².In the numerator we have (1 + 2√3) (2+√3). Now we can multiply this using distributive property.

By comparing this we get x =  8 and y = 5 as the final answer.


Question 4

Rationalize the denominator (3 + √5)/(3 - √5) + (3 - √5)/(3 + √5) =

x + y √5 and find the value of x and y.

Solution

L.H.S

We have two fractions in the given question. We have to take L.C.M to add both the fractions. Now the denominator is like in the form (a+ b) (a-b). So we have simplified this using a² - b².In the numerator we have  (3+√5)² and (3-√5)².This exactly matches with the formulas (a+b)² and (a-b)². We have expanded by using formula a² + 2ab + b² and a² - 2ab + b². rationalizing the denominator solution4 rationalizing the denominator solution4

By combining the we get 7 as answer.But here after we need to compare this with R.H.S to get the values of x and y.


Question 5

Rationalize the denominator

(√5-√7)/(√5 + √7) - (√5 + √7)/(√5 - √7) = x + y √35

and find the value of x and y.

Solution

L.H.S

We have two fractions in the given question. We have to take L.C.M to add both the fractions. Now the denominator is like in the form (a+ b) (a-b). So we have simplified this using a² - b².In the numerator we have  (√5-√7)² and (√5+7)².This exactly matches with the formulas (a-b)² and (a+b)². We have expanded by using formula a² - 2ab + b² and a² + 2ab + b².

By combining the we get 4√35/2 as answer.But here after we need to compare this with R.H.S to get the values of x and y.

By comparing this we get x =  0 and y = 2 as the final answer.