Question

Pls answer the question with correct steps

Answer 1

1. i) 1/√7

To rationalize it we must multiply numerator and denominator with √7

= (1 ×√7)/(√7×√7)
= √7/ 7

ii) 1/(√7-2)
To rationalize this we will multiply it's denominator and numerator with √7+2

={1 ×(√7+2) }/ (√7-2)(√7+2)
= (√7 +2) / (7-4) [as a^2 -b^2 = (a+b)(a-b)]
= (√7 +2)/3
= (√7+2) /3

2. Given that √2 = 1.4142
(√2 -1)/(√2+1)

By Rationalizing the denominator
(√2 -1)(√2-1)/ (√2+1)(√2-1)
=(2-√2) ( 2-√2)/ 2-1
root ( 2-√2) ( 2-√2) = ( 2-√2)


By putting the value of √2 as 1.4142

= 2- (1.4142)
= 2- 1.4142
=0.5858


3. Given that
x = 2+√3
Then 1/x
= 1/(2+√3)
By Rationalizing the denominator
= 1( 2-√3)/( 2-√3)(2+√3)
= 2 - √3 ) / (4-3)
= 2-√3

So, 1/x=1/(2+√3) = 2-√3

x + 1/ x

= (2+√3) +(2-√3)
= 2+2
= 4