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How do you find the square root of 5 to the 3rd power?

1 Answer

Sep 10, 2015

${(\sqrt{5})}^{3} \approx 11.18$ $(sqrt5)^3approx color(green)(11.18$

Explanation:

square root of 5 to the 3rd power can be written as
${(\sqrt{5})}^{3}$ $(sqrt5)^3$

$= \sqrt{5} \cdot \sqrt{5} \cdot \sqrt{5}$ $= sqrt5*sqrt5*sqrt5$

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

Hence $\sqrt{5} \cdot \sqrt{5} \cdot \sqrt{5} = 5 \sqrt{5}$ $sqrt5*sqrt5*sqrt5 = 5 sqrt5$

$\sqrt{5} \approx 2.236$ $sqrt5 approx2.236$

So $5 \sqrt{5} \approx 5 \cdot (2.236) \approx 11.18$ $5 sqrt5 approx 5*(2.236) approx color(green)(11.18$

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