Question

6-4√2/6+4√2 , Simplify the given number by rationalising the denominator.

Answer 1

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

Answer 2

Solution :

(6-4√2)/(6+4√2)

= [2(3-2√2)]/[2(3+2√2)]

= (3-2√2)/(3+2√2)

Rationalise the denominator,

=[(3-2√2)(3-2√2)/(3+2√2)(3-2√2)]

= (3-2√2)²/[3² - (2√2)²]

[ Since , x²-y² = (x+y)(x-y)]

= [3²- 2×3×2√2 + (2√2)²]/(9-8)

= ( 9 - 12√2 + 8 )/1

= 17 - 12√2

••••