Question

Rationalise the denominators of
3-2 root2/ 3+2 root2

Answer 1

(3-2 root 2)/ (3+ 2 root 2 )

as we rationalise denominator, we multiply both numerator and denominator by 3-2root2


so, numerator becomes (3-2root2)^2 and denominator becomes (3+2root2)(3-2root2) = 3^2-(2root2)^2 = 9 -8 =1


as the denominator is 1, we just have to find numerator = (3-2root2)^2 = 3^2 + (2root2)^2 - (2)(3)(2root2) = 9+8 - 12 root2 = 17 - 12 root

so, 17 - 12 root 2 is the answer

Answer 2

Hello Dear!!!

Here's your answer

3-2√2 / 3+2√2

Multiply the numerator and denominator with conjugate of denominator.

Conjugate of denominator is 3-2√2


3-2√2 / (3+2√2) * (3-2√2)/(3-2√2)

(3-2√2)^2 / {(3)^2 - (4*2)}

{(3)^2 + 8 - 2*3*2√2 } / 9-8

9 + 8 - 12√2 / 1

17-12√2

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The formulas used are

(a-b)^2 = (a)^2 + (b)^2 - 2ab .... in 3rd step

(a+b)(a-b) = (a)^2 - (b)^2..... in 3rd step


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Hope this helps you....