How do you simplify $5sqrt(54)$ ?

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Answer 1 · 2017-03-05T01:14:31

$5 sqrt(54) = 15sqrt(6)$

Note that if $a, b >= 0$ we have:

$sqrt(ab) = sqrt(a)sqrt(b)$

Factor $54$ to identify square factors:

$54 = 2*3^3 = 3^2*6$

Hence:

$5 sqrt(54) = 5 sqrt(3^2 * 6) = 5sqrt(3^2)sqrt(6) = 5*3sqrt(6) = 15sqrt(6)$

This is the simplest form of the square root.

How do you simplify 5sqrt(54)5sqrt(54) ?