Question

Simplify each of the following by rationalizing the denominator 6-4√2\6+4√2

Answer 1

The simplified form of given expression is $17 - 12\sqrt{2}$.

Step-by-step explanation:

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

Hence, the simplified form of given expression is $17 - 12\sqrt{2}$.