Question

How 48root 2 came in 6-4 root 2 / 6+4 root 2

Answer 1

Step-by-step explanation:

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

6+4

2

6−4

2

=17−12

2

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

6+4

2

6−4

2

Now, we need to rationalise the above fraction.

To rationalise \frac{6-4 \sqrt{2}}{6+4 \sqrt{2}}

6+4

2

6−4

2

, multiply the numerator by 6-4 \sqrt{2}6−4

2

and denominator by 6-4 \sqrt{2}6−4

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}

6+4

2

6−4

2

×

6−4

2

6−4

2

=

36−32

36+32−48

2

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

4

68−48

2

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}}\italic

6+4

2

6−4

2

=17−12

2