# How do you multiply and simplify by factoring sqrt10*sqrt35?

Jan 11, 2017

$5 \sqrt{14}$

#### Explanation:

Introductory note: $\sqrt{a \times b} \text{ is the same as } \sqrt{a} \times \sqrt{b}$

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Given:$\text{ "sqrt10" "xx" } \sqrt{35}$

Write as: $\text{ "sqrt(2xx5)" "xx" } \sqrt{5 \times 7}$

Which is also the same as:$\text{ } \sqrt{2} \times \sqrt{5} \times \sqrt{5} \times \sqrt{7}$

But $\sqrt{5} \times \sqrt{5} = 5$ giving:$\text{ } 5 \sqrt{2} \times \sqrt{7}$

but this is the same as:$\text{ "5sqrt(2xx7)" "=" } 5 \sqrt{14}$

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Check:

$\text{ } 5 \sqrt{14} \approx 18.70828 \ldots \ldots$

$\sqrt{10} \times \sqrt{35} \approx 18.70828 \ldots \ldots$