# Find the value of (2sqrt6)^6?

Aug 16, 2017

${\left(2 \sqrt{6}\right)}^{6} = 13824$

#### Explanation:

${\left(2 \sqrt{6}\right)}^{6}$

= ${2}^{6} \times {\left(\sqrt{6}\right)}^{6}$

= $\left(2 \times 2 \times 2 \times 2 \times 2 \times 2\right) \times \left(\sqrt{6 \times 6 \times 6 \times 6 \times 6 \times 6}\right)$

= $64 \times \sqrt{\underline{6 \times 6} \times \underline{6 \times 6} \times \underline{6 \times 6}}$

= $64 \times 6 \times 6 \times 6$

= $64 \times 216$

= $13824$

Aug 16, 2017

$13 , 824$

#### Explanation:

Use the laws of indices.

${\left(2 \sqrt{6}\right)}^{6} = {2}^{6} \times {\left(\sqrt{6}\right)}^{6} \text{ } \leftarrow \left({\left(a b\right)}^{m} = {a}^{m} {b}^{m}\right)$

$= {2}^{6} \times {\left(6\right)}^{\frac{6}{2}} \text{ } \leftarrow \sqrt{x} = {x}^{\frac{1}{2}}$

$= {2}^{6} \times {6}^{3}$

$= \left(2 \times 2 \times 2 \times 2 \times 2 \times 2\right) \times \left(6 \times 6 \times 6\right)$

It helps to know the powers less than 1000 by heart.

$= 64 \times 216$

$= 13 , 824$

Jun 21, 2018

$13824$

#### Explanation:

${\left(2 \sqrt{6}\right)}^{6}$

$\therefore = {\left(2 \times {6}^{\frac{1}{2}}\right)}^{6}$

$\therefore = {2}^{6} \times {6}^{\frac{6}{2}}$

$\therefore = 64 \times {6}^{3}$

$\therefore = 64 \times 216$

$\therefore = 13824$