# What is the square root of 5 times the square root of 35?

May 30, 2018

What is: $\sqrt{5} \times \sqrt{35}$?

#### Explanation:

Use this rule for radicals to combine the terms:

$\sqrt{\textcolor{red}{a}} \cdot \sqrt{\textcolor{b l u e}{b}} = \sqrt{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}}$

$\sqrt{\textcolor{red}{5}} \cdot \sqrt{\textcolor{b l u e}{35}} \implies \sqrt{\textcolor{red}{5} \cdot \textcolor{b l u e}{35}} \implies \sqrt{175}$

Next, we can rewrite the term under the radical as:

$\sqrt{25 \cdot 7}$

Now, use this rule for radicals to simplify the expression:

$\sqrt{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}} = \sqrt{\textcolor{red}{a}} \cdot \sqrt{\textcolor{b l u e}{b}}$

$\sqrt{\textcolor{red}{25} \times \textcolor{b l u e}{7}} \implies \sqrt{\textcolor{red}{25}} \times \sqrt{\textcolor{b l u e}{7}} \implies 5 \times \sqrt{7} \implies 5 \sqrt{7}$

May 30, 2018

$5 \sqrt{7}$

#### Explanation:

$\sqrt{5} \cdot \sqrt{35} = \sqrt{5 \cdot 35} = \sqrt{175}$

Note that we now have among the factors of 175 a square under the square root that we can take out to simplify

$\sqrt{175} = \sqrt{{5}^{2} \cdot 7} = 5 \sqrt{7} \cdot$

It is usually worth keeping track of what factors go in in advance - so in this case remembering that $35 = 5 \cdot 7$.