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How do you simplify √150 ÷ √3?

1 Answer

Jul 23, 2015

$= 5 \sqrt{2}$ $=color(blue)(5sqrt2$

Explanation:

Prime factorising: $\sqrt{150} = \sqrt{3 \cdot 5 \cdot 2 \cdot 5}$ $sqrt150 = sqrt(3*5*2*5)$

$= 5 \sqrt{6}$ $=5sqrt6$

Now:
$\frac{\sqrt{150}}{\sqrt{3}} = \frac{5 \sqrt{6}}{\sqrt{3}}$ $sqrt150/sqrt3 = (5sqrt6)/sqrt3$

$\sqrt{6} = \sqrt{2} \cdot \sqrt{3}$ $sqrt 6 =sqrt2 * sqrt3$

So,
$(5sqrt6)/sqrt3 = (5cancelsqrt3*sqrt2)/cancelsqrt3$

$=color(blue)(5sqrt2$

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