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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