Question

Rationalize the denominator of 6-4√2 / 6+4√2​

Answer 1

here's your answer

hope it helps you

Answer 2

TO RATIONALISE THE DENOMINATOR

$\frac{6 - 4 \sqrt{2} }{6 + 4 \sqrt{2} }$

ANSWER

First we have to multiply the denominator of the fraction with such a factor that the irrational get converted into rational

The factor shall be apply to use

(a+b)(a-b)= a^2 - b^2 Identity.

The factor should be multiply in both numerator and denominator so that the value remain same.

$\frac{6 - 4 \sqrt{2} }{6 + 4 \sqrt{2} } \times 1 \\ \\ \\ \\ = \frac{6 - 4 \sqrt{2} }{6 + 4 \sqrt{2} } \times \frac{6 - 4 \sqrt{2} }{6 - 4 \sqrt{2} } \\ \\ \\ \\ = \frac{ {(6 - 4 \sqrt{2)} }^{2} }{ {6}^{2} - {(4 \sqrt{2} )}^{2} } \\ \\ \\ \\ = \frac{36 + 32 - 48 \sqrt{2} }{36 - 32} \\ \\ \\ \\ = \frac{68 - 48 \sqrt{2} }{4} \\ \\ \\ \\ = \frac{4(17 - 12 \sqrt{2} )}{4} \\ \\ \\ \\ = \boxed{17 - 12 \sqrt{2} }$

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