# How do you simplify sqrt(35) xx sqrt(15)?

Apr 5, 2018

$5 \sqrt{21}$

#### Explanation:

You can 'split' roots

$\sqrt{5 \times 7} \times \sqrt{3 \times 5}$

$\sqrt{5} \times \sqrt{7} \times \sqrt{3} \times \sqrt{5}$

$\sqrt{5} \times \sqrt{5} \times \sqrt{3 \times 7}$

$5 \sqrt{21}$
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Lets test this approach with numbers we know

$\sqrt{16} = 4 \text{ }$ Technically it is $\pm 4$ but lets ignore that.

$\sqrt{4 \times 4} = \sqrt{4} \times \sqrt{4} = 2 \times 2 = 4$