How do you simplify $\sqrt{5} (\sqrt{2} + 4 \sqrt{2})$ $sqrt5(sqrt2+4sqrt2)$ ?

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Answer 1 · 2017-08-22T12:45:58

See a solution process below:

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

$\sqrt{5} (\sqrt{2} + 4 \sqrt{2}) \Rightarrow$ $sqrt(5)(sqrt(2) + 4sqrt(2)) =>$

$\sqrt{5} \sqrt{2} (1 + 4) \Rightarrow$ $sqrt(5)sqrt(2)(1 + 4) =>$

$\sqrt{5} \sqrt{2} (5) \Rightarrow$ $sqrt(5)sqrt(2)(5) =>$

$5 \sqrt{5} \sqrt{2}$ $5sqrt(5)sqrt(2)$

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

$\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$ $sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))$

$5 \sqrt{5 \cdot 2}$ $5sqrt(5 * 2)$

$5 \sqrt{10}$ $5sqrt(10)$

How do you simplify √5(√2+4√2)sqrt5(sqrt2+4sqrt2)?