How do you simplify $sqrt5(sqrt2+4sqrt2)$ ?

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Answer 1 · 2017-08-22T12:45:58

See a solution process below:

First, we can factor a $sqrt(2)$ out of each term in the parenthesis:

$sqrt(5)(sqrt(2) + 4sqrt(2)) =>$

$sqrt(5)sqrt(2)(1 + 4) =>$

$sqrt(5)sqrt(2)(5) =>$

$5sqrt(5)sqrt(2)$

We can now use this rule for radicals to simplify the radicals:

$sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))$

$5sqrt(5 * 2)$

$5sqrt(10)$

How do you simplify sqrt5(sqrt2+4sqrt2)sqrt5(sqrt2+4sqrt2)?