## Rationalizing the Denominator Solution3

In this page rationalizing the denominator solution3 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 1

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

Solution

L.H.S

In this question we have 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  (2+√3)² .This exactly matches with the formula (a+b)². We have expanded by using formula a² + 2ab + b². By simplifying this we get (7+4√3). Now we have to compare the final answer with R.H.S

By comparing this we get x =  7 and y = 4 as the final answer.

Question 2

Rationalize the denominator (5 + 4√3)/(4 + 5√3) = x + y √3 and find the value of x and y.

Solution

L.H.S

In this question we have 5 + 4√3 in the numerator and 4 + 5√3 in the denominator so we have to multiply by its conjugate that is 4 - 5 √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 (5 + 4√3)(4 - 5√3) We have multiplied this using distributive property. Then we are going to combine the like terms.

By simplifying this we get (40+9√3)/59. Now we have to compare the final answer with R.H.S to get the value of x and y.rationalizing the denominator solution3 rationalizing the denominator solution3

By comparing this we get x =  40/59 and y = 9/59 as the final answer.

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