The number obtained on rationalising the denominator of 1/(√7 - 2) is
a. (√7 + 2)/3
b. (√7 - 2)/3
c. (√7 + 2)/5
d. (√7 + 2)/45
Solution:
Given
1/(√7 - 2)
Let us multiply both numerator and denominator by √7 + 2
= 1/(√7 - 2) x (√7 + 2)/(√7 + 2)
Using the algebraic identity (a + b) (a - b) = a² - b²
= (√7 + 2)/ (7 - 4)
By further calculation
= (√7 + 2)/ 3
Therefore, the number obtained is (√7 + 2)/ 3.
✦ Try This: The number obtained on rationalising the denominator of 1/(√5 - 2) is
Given
1/(√5 - 2)
Let us multiply both numerator and denominator by √5 + 2
= 1/(√5 - 2) x (√5 + 2)/(√5 + 2)
Using the algebraic identity (a + b) (a - b) = a² - b²
= (√5 + 2)/ (5 - 4)
By further calculation
= (√5 + 2)/ 1
Therefore, the number obtained is (√5 + 2).
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1
NCERT Exemplar Class 9 Maths Exercise 1.1 Problem 12
The number obtained on rationalising the denominator of 1/(√7 - 2) is a. (√7 + 2)/3, b. (√7 - 2)/3, c. (√7 + 2)/5, d. (√7 + 2)/45
Summary:
The number obtained on rationalising the denominator of 1/(√7 - 2) is (√7 + 2)/ 3
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