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.

**Quest****ion 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.

**Quest****ion 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.

**Quest****ion 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.