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What is the square root of 12 times the square root of 3?

1 Answer

Sep 11, 2015

(Assuming only principal [non-negative] square roots
$\sqrt{12} \times \sqrt{3} = 6$ $sqrt(12)xxsqrt(3) = 6$

Explanation:

$\sqrt{12} = \sqrt{2^{2} \times 3} = \sqrt{2^{2}} \times \sqrt{3} = 2 \sqrt{3}$ $sqrt(12) = sqrt(2^2xx3) = sqrt(2^2)xxsqrt(3) = 2sqrt(3)$

So $\sqrt{12} \times \sqrt{3}$ $sqrt(12)xxsqrt(3)$
$XXX = 2 \sqrt{3} \times \sqrt{3}$ $color(white)("XXX")=2sqrt(3)xxsqrt(3)$

$XXX = (2 \times \sqrt{3}) \times \sqrt{3})$ $color(white)("XXX")=(2xx sqrt(3))xxsqrt(3))$

$XXX = 2 \times (\sqrt{3} \times \sqrt{3})$ $color(white)("XXX")=2xx (sqrt(3)xxsqrt(3))$

$XXX = 2 \times 3$ $color(white)("XXX")=2xx3$

$XXX = 6$ $color(white)("XXX")=6$

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