How do you simplify $\sqrt{\frac{3}{16}} \cdot \sqrt{\frac{9}{5}}$ $sqrt(3/16)*sqrt(9/5)$ ?

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How do you simplify $\sqrt{\frac{3}{16}} \cdot \sqrt{\frac{9}{5}}$ $sqrt(3/16)*sqrt(9/5)$ ?

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Answer 1 · 2017-04-23T07:24:24

$\sqrt{\frac{3}{16}} \cdot \sqrt{\frac{9}{5}} = \frac{3 \sqrt{15}}{20}$ $sqrt(3/16)*sqrt(9/5) = (3sqrt(15))/20$

Explanation:

Note that if $a, b \geq 0$ $a, b >= 0$ then:

$\sqrt{a b} = \sqrt{a} \sqrt{b}$ $sqrt(ab) = sqrt(a)sqrt(b)$

If $a > 0$ $a > 0$ and $b \geq 0$ $b >= 0$ then:

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ $sqrt(a/b) = sqrt(a)/sqrt(b)$

If $a \geq 0$ $a >= 0$ then:

$\sqrt{a^{2}} = a$ $sqrt(a^2) = a$

When simplifying square roots of rational expressions, I like to make the denominator square before splitting the square root. That way we don't have to rationalise the denominator later...

$\sqrt{\frac{3}{16}} \cdot \sqrt{\frac{9}{5}} = \sqrt{\frac{3}{16}} \cdot \sqrt{\frac{9 \cdot 5}{5 \cdot 5}}$ $sqrt(3/16)*sqrt(9/5) = sqrt(3/16)*sqrt((9*5)/(5*5))$

$\sqrt{\frac{3}{16}} \cdot \sqrt{\frac{9}{5}} = \sqrt{\frac{3}{4^{2}}} \cdot \sqrt{\frac{45}{5^{2}}}$ $color(white)(sqrt(3/16)*sqrt(9/5)) = sqrt(3/4^2)*sqrt(45/5^2)$

$\sqrt{\frac{3}{16}} \cdot \sqrt{\frac{9}{5}} = \sqrt{\frac{3 \cdot 45}{4^{2} \cdot 5^{2}}}$ $color(white)(sqrt(3/16)*sqrt(9/5)) = sqrt((3*45)/(4^2*5^2))$

$\sqrt{\frac{3}{16}} \cdot \sqrt{\frac{9}{5}} = \frac{\sqrt{3 \cdot 45}}{\sqrt{4^{2} \cdot 5^{2}}}$ $color(white)(sqrt(3/16)*sqrt(9/5)) = sqrt(3*45)/sqrt(4^2*5^2)$

$\sqrt{\frac{3}{16}} \cdot \sqrt{\frac{9}{5}} = \frac{\sqrt{3 \cdot 3^{2} \cdot 5}}{\sqrt{{(4 \cdot 5)}^{2}}}$ $color(white)(sqrt(3/16)*sqrt(9/5)) = sqrt(3*3^2*5)/sqrt((4*5)^2)$

$\sqrt{\frac{3}{16}} \cdot \sqrt{\frac{9}{5}} = \frac{\sqrt{3^{2}} \cdot \sqrt{15}}{\sqrt{20^{2}}}$ $color(white)(sqrt(3/16)*sqrt(9/5)) = (sqrt(3^2)*sqrt(15))/sqrt(20^2)$

$\sqrt{\frac{3}{16}} \cdot \sqrt{\frac{9}{5}} = \frac{3 \sqrt{15}}{20}$ $color(white)(sqrt(3/16)*sqrt(9/5)) = (3sqrt(15))/20$

Answer 2 · 2017-04-23T10:05:03

$\frac{3 \sqrt{15}}{20}$ $(3sqrt15)/20$

Explanation:

$\sqrt{\frac{3}{16}} \cdot \sqrt{\frac{9}{5}}$ $sqrt(3/16)*sqrt(9/5)$

$:.=sqrt3/sqrt16*sqrt9/sqrt5$

$:.=sqrt3/sqrt(4*4)*sqrt(3*3)/sqrt5$

$:.sqrt4*sqrt4=4,sqrt3*sqrt3=3$

$:.=sqrt3/4*3/sqrt5$

$:.=(3sqrt3)/(4sqrt5)*sqrt5/sqrt5$

$:.=sqrt5*sqrt5=5$

$:.=(3sqrt15)/(4*5)$

$:.=(3sqrt15)/20$

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How do you simplify $\sqrt{\frac{3}{16}} \cdot \sqrt{\frac{9}{5}}$ $sqrt(3/16)*sqrt(9/5)$ ?

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