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# 1/ (√9 - √8) is equal to

a. 1/2 (3 - 2√2)

b. 1/(3 + 2√2)

c. 3 - 2√2

d. 3 + 2√2

**Solution:**

Given

1/ (√9 - √8)

We can write it as

= 1/ (3 - 2√2)

Let us multiply both __numerator__ and __denominator__ by 3 + 2√2

= 1/ (3 - 2√2) × (3 + 2√2)/(3 + 2√2)

Using the __algebraic identity__ (a + b) (a - b) = a² - b²

= (3 + 2√2)/ (9 - 8)

By further calculation

= (3 + 2√2)/ 1

= 3 + 2√2

Therefore, the number obtained is (3 + 2√2).

**✦ Try This: **1/ (√25 - √20) is equal to

Given

1/ (√25 - √20)

We can write it as

= 1/ (5 - 2√5)

Let us multiply both numerator and denominator by 5 + 2√5

= 1/ (5 - 2√5) × (5 + 2√5)/(5 + 2√5)

Using the algebraic identity (a + b) (a - b) = a² - b²

= (5 + 2√5)/ (25 - 20)

By further calculation

= (5 + 2√5)/ 5

Taking √5 as common

= (√5 + 2)/√5

Therefore, the number obtained is (√5 + 2)/√5.

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 1

**NCERT Exemplar Class 9 Maths Exercise 1.1 Problem 13**

## 1/ (√9 - √8) is equal to a. 1/2 (3 - 2√2), b. 1/(3 + 2√2), c. 3 - 2√2, d. 3 + 2√2

**Summary**:

The number obtained on rationalising the denominator of 1/ (√9 - √8) is equal to 3 + 2√2

**☛ Related Questions:**

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