In this page rationalizing the denominator solution1 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 1**

**Rationalize the denominator ****1/(****2 + √5)**

**Solution**

**Explanation:**

In this question we have 2 + √5 in the denominator
so we have to multiply by its conjugate that is 2 - √5 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.By simplifying this
we get (√5-2)/3 as answer.

**Quest****ion 2**

**Rationalize the denominator ****(6****+ √5)**/(6** - √5)**

**Solution**

**Explanation:**

In this question we have 6 + √5 in the numerator and 6 - √5 in the denominator
so we have to multiply by its conjugate that is 6 + √5 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 denominator (6 + √5)². So we have expanded this using algebraic identity (a+b)² = a² + 2ab +b². By simplifying this
we get 41+ 12√5 as answer.

**Quest****ion 3**

**Rationalize the denominator ****1****/(****√2 +** √3) and also find the

**approximate value using √2 = 1.414 and √3 = 1.732**

**Solution**

**Explanation:**

In this question we have √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.By simplifying this we get √3-√2 as answer.

= 1.732- 1.414

= **0.318**

The approximate value of the rational number 1/√2 + √3 is 0.318.

**Quest****ion 4**

**Rationalize the denominator ****(****√2 + 1)**/(**√2 - 1)**

**Solution**

**Explanation:**

In
this question we have √2 + 1 in the numerator and √2 - 1 in the
denominator
so we have to multiply by its conjugate that is √2 + 1 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 denominator
(√2 + 1)². So we have expanded this using algebraic identity (a+b)² = a²
+
2ab +b². By simplifying this
we get 3 - 2√2 as answer. rationalizing the denominator solution1