Rationalizing the Denominator Solution1

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.

Question 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.

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Question 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.

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Question 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.

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Question 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