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What is the square root of 10 times the square root of 35?

1 Answer

Sep 17, 2015

$\sqrt{10} \times \sqrt{35} = 5 \sqrt{14}$ $sqrt(10)xxsqrt(35)=5sqrt(14)$

Explanation:

$\sqrt{10} = \sqrt{2} \times \sqrt{5}$ $color(red)(sqrt(10) =sqrt(2)xxsqrt(5))$

$\sqrt{35} = \sqrt{5} \times \sqrt{7}$ $color(blue)(sqrt(35) = sqrt(5)xxsqrt(7))$

$\sqrt{10} \times \sqrt{35}$ $sqrt(10)xxsqrt(35)$

$= (\sqrt{2} \times \sqrt{5}) \times (\sqrt{5} \times \sqrt{7})$ $=color(red)((sqrt(2)xxsqrt(5)))xxcolor(blue)((sqrt(5)xxsqrt(7))$

$= (\sqrt{5} \times \sqrt{5}) \times (\sqrt{2} \times \sqrt{7})$ $=(color(red)(sqrt(5))xxcolor(blue)(sqrt(5)))xx(color(red) (sqrt(2))xxcolor(blue)(sqrt(7)))$

$= 5 \times \sqrt{14}$ $=5xxsqrt(14)$

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