How do you simplify the expression $sqrt3*3sqrt21$ ?

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Answer 1 · 2016-04-01T16:15:53

$9sqrt(7)$

Note that $3xx7=21$

So write the expression as:

$color(blue)(sqrt(3))color(brown)(xx3sqrt(3xx7))$

Combine the square roots

$3sqrt(3xx3xx7)$

$3sqrt(3^2xx7)$

Not that $sqrt(3^2)=3$

$3xx3sqrt(7)$

$9sqrt(7)$

$color(red)("Technically this could be "+-9sqrt(7))$

How do you simplify the expression sqrt3*3sqrt21sqrt3*3sqrt21?