What is the square root of 20 times the square root of 15?

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Answer 1 · 2015-09-08T12:39:03

$\sqrt{4 \cdot 5} \cdot \sqrt{15} = 10 \sqrt{3} ~ 17.321$ $sqrt(4*5)*sqrt(15)=color(green)( 10sqrt 3 ~ 17.321$

square root of 20 times the square root of 15 in mathematical terms can be written as $\sqrt{20} \cdot \sqrt{15}$ $sqrt20 * sqrt15$

= $\sqrt{4 \cdot 5} \cdot \sqrt{15}$ $sqrt(4*5)*sqrt(15)$

We know that $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$ $color(blue)(sqrt(a*b) = sqrta*sqrtb)$

Hence = $\sqrt{4 \cdot 5} \cdot \sqrt{15} = \sqrt{4} \cdot \sqrt{5} \cdot \sqrt{3} \cdot \sqrt{5}$ $sqrt(4*5)*sqrt(15) = sqrt4*sqrt5*sqrt3*sqrt5$

$= 2 \cdot {(\sqrt{5})}^{2} \cdot \sqrt{3}$ $= 2*(sqrt5)^2*sqrt3$

$= 2 \cdot 5 \cdot \sqrt{3}$ $= 2* 5 *sqrt3$

$= 10 \sqrt{3}$ $=color(green)( 10sqrt 3$