Question

16 divide root 2 -35 divide root 50 -2 root 18 + 3 root 72​

Answer 1

Given:

The expression is:

$\dfrac{16}{\sqrt{2}}-\dfrac{35}{\sqrt{50}}-2\sqrt{18}+3\sqrt{72}$

To find:

The simplified form of the given expression.

Solution:

We have,

$\dfrac{16}{\sqrt{2}}-\dfrac{35}{\sqrt{50}}-2\sqrt{18}+3\sqrt{72}$

It can be written as:

$=\dfrac{16}{\sqrt{2}}-\dfrac{35}{\sqrt{25\times 2}}-2\sqrt{9\times 2}+3\sqrt{36\times 2}$

$=\dfrac{16}{\sqrt{2}}-\dfrac{35}{5\sqrt{2}}-2\times 3\sqrt{2}+3\times 6\sqrt{2}$

Rationalizing the denominator, we get

$=\dfrac{16}{\sqrt{2}}\times \dfrac{\sqrt{2}}{\sqrt{2}}-\dfrac{35}{5\sqrt{2}}\times \dfrac{\sqrt{2}}{\sqrt{2}}-6\sqrt{2}+18\sqrt{2}$

$=\dfrac{16\sqrt{2}}{2}-\dfrac{35\sqrt{2}}{5\times 2}-6\sqrt{2}+18\sqrt{2}$

$=8\sqrt{2}-\dfrac{7\sqrt{2}}{2}+12\sqrt{2}$

$=20\sqrt{2}-\dfrac{7\sqrt{2}}{2}$

Taking LCM, we get

$=\dfrac{40\sqrt{2}-7\sqrt{2}}{2}$

$=\dfrac{33\sqrt{2}}{2}$

Therefore, the simplified form of the given expression is $\dfrac{33\sqrt{2}}{2}$.