How do you simplify $-3sqrt(252)$ ?

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Answer 1 · 2015-07-27T12:29:55

$=color(blue)(−18sqrt(7)$

$−3sqrt252$

Prime factorising $252$

$=−3sqrt(2*2*3*3*7)$

$=−3sqrt(2^2 *3^2*7)$
$=−3(2*3)sqrt(7)$

$=color(blue)(−18sqrt(7)$

Answer 2 · 2015-07-27T12:33:35

You check to see if you can write $252$ as a product of a perfect square and another number.

Since $252$ is not a perfect square itself, you can check to see if you can write it as a product of a perfect square and another number.

To do that, find the prime factors of $252$

${(252 : 2 = 126), (126 : 2 = 63) :} -> 2^2$

${(63 : 3= 21), (21 : 3 = 7) :} -> 3^2$

$7 : 7 = 1 -> 7^1$

So, you can write $252$ as

$252 = 2^2 * 3^2 * 7 = 4 * 9 * 7 = underbrace(36)_(color(blue)(=6^2)) * 7$

This means that the original expression will be equivalent to

$-3 * sqrt(252) = -3 * sqrt(36 * 7)$

$-3 * sqrt(36) * sqrt(7) = -3 * 6 * sqrt(7) = color(green)(-18sqrt(7))$

How do you simplify -3sqrt(252)-3sqrt(252)?