Question

Rationalise 6-4 root 2 /6+4 root 2

Answer 1

To rationalize it we need to multiply it's denominator and numerator with 6-4√2


(6-4√2) (6-4√2) / (6+4√2)(6-4√2)

=( 36 + 32 - 48√2)/ ( 36 - 32)
= (68-48√2) / (4)
= 4 (17-12√2)/ 4
= 17-12√2

Answer 2

Rationalise of $\bold{\frac{6-4\sqrt{2}}{6+4\sqrt{2} }=17-12\sqrt{2}}$

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

Now, we need to rationalise the above fraction.

To rationalise $\frac{6-4 \sqrt{2}}{6+4 \sqrt{2}}$  , multiply the numerator by $6-4 \sqrt{2}$ and denominator by $6-4 \sqrt{2}$

Now, the whole numbers are multiplied with the whole numbers in the numerator.

Now, we get, $\frac{6-4 \sqrt{2}}{6+4 \sqrt{2}} \times \frac{6-4 \sqrt{2}}{6-4 \sqrt{2}}=\frac{36+32-48 \sqrt{2}}{36-32}$

On simplifying the above step, we get = $\frac{68-48 \sqrt{2}}{4}$  

On further simplification of the above step, we get the answer as,

$\italic{\frac{6-4\sqrt{2}}{6+4\sqrt{2} }=17-12\sqrt{2}}$