Find the value of ${(2 \sqrt{6})}^{6}$ $(2sqrt6)^6$ ?

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Find the value of ${(2 \sqrt{6})}^{6}$ $(2sqrt6)^6$ ?

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Answer 1 · 2017-08-16T13:30:10

${(2 \sqrt{6})}^{6} = 13824$ $(2sqrt6)^6=13824$

Explanation:

${(2 \sqrt{6})}^{6}$ $(2sqrt6)^6$

= $2^{6} \times {(\sqrt{6})}^{6}$ $2^6xx(sqrt6)^6$

= $(2 \times 2 \times 2 \times 2 \times 2 \times 2) \times (\sqrt{6 \times 6 \times 6 \times 6 \times 6 \times 6})$ $(2xx2xx2xx2xx2xx2)xx(sqrt(6xx6xx6xx6xx6xx6))$

= $64 \times \sqrt{6 \times 6 - --- - \times 6 \times 6 - --- - \times 6 \times 6 - --- -}$ $64xxsqrt(ul(6xx6)xxul(6xx6)xxul(6xx6))$

= $64xx6xx6xx6$

= $64xx216$

= $13824$

Answer 2 · 2017-08-16T14:55:05

$13,824$

Explanation:

Use the laws of indices.

$(2 sqrt6)^6 = 2^6 xx (sqrt6)^6" "larr ((ab)^m = a^m b^m)$

$=2^6 xx (6)^(6/2)" "larr sqrtx = x^(1/2)$

$=2^6 xx 6^3$

$=(2xx2xx2xx2xx2xx2)xx (6xx6xx6)$

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

$= 64 xx 216$

$=13,824$

Answer 3 · 2018-06-21T17:33:02

$13824$

Explanation:

$(2 sqrt 6)^6$

$:.=(2 xx6^(1/2))^6$

$:.=2^6 xx6^(6/2)$

$:.=64 xx 6^3$

$:.=64 xx 216$

$:.=13824$

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