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How do you simplify ${(5 \sqrt{3})}^{2}$ $(5sqrt3)^2$ ?

1 Answer

May 8, 2016

${(\sqrt{3})}^{2} = 75$ $(sqrt(3))^2 = color(blue)(75)$

Explanation:

Note that for the general case:
$XXX {(a b)}^{2} = a^{2} \cdot b^{2}$ $color(white)("XXX")(ab)^2 = a^2*b^2$

So
$XXX {(5 \sqrt{3})}^{2} = 5^{2} \cdot {(\sqrt{3})}^{2}$ $color(white)("XXX")(5sqrt(3))^2 = 5^2 * (sqrt(3))^2$

$XXXXXXX = 25 \cdot 3$ $color(white)("XXXXXXX")=25 * 3$

$XXXXXXX = 75$ $color(white)("XXXXXXX")= 75$

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