How do you simplify $sqrt(28a^2b^3)$ ?

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Answer 1 · 2016-10-17T17:50:28

$2sqrt7ab^(3/2)$

The easiest way to simplify this surd is to separate it into its constituent surds, that is, the surds that make it up:

$sqrt(ab) = sqrtaxxsqrtb$

So if we apply the same rule to $sqrt(28a^2b^3)$ we get:

$sqrt(28a^2b^3) = sqrt28xxsqrt(a^2)xxsqrt(b^3$

We can do this again with each of these surds to simplify it again:

$sqrt28xxsqrt(a^2)xxsqrt(b^3) =sqrt4xxsqrt7xxsqrtaxxsqrtaxxsqrtbxxsqrtbxxsqrtb$

We can evaluate these surds by separating them into like factors:

$sqrt4xxsqrt7=2xxsqrt7=2sqrt7$
$sqrtaxxsqrta=a$
$sqrtbxxsqrtbxxsqrtb=bsqrtb=b^(3/2)$

Now we need to multiply each of these factors:

$2sqrt7ab^(3/2)$

How do you simplify sqrt(28a^2b^3)sqrt(28a^2b^3)?