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How do you find the square root of 81/16?

1 Answer

Jun 7, 2016

$= \frac{9}{4}$ $= color(blue)(9/4$

Explanation:

$\sqrt{\frac{81}{16}}$ $sqrt (81/16)$

We simplify $81$ $81$ and $16$ $16$ by prime factorisation (expressing a number as a product of its prime factors).

$\sqrt{81} = \sqrt{3 \cdot 3 \cdot 3 \cdot 3} = \sqrt{9 \cdot 9} = \sqrt{9^{2}} = 9$ $sqrt (81) = sqrt (3 * 3 * 3 * 3 ) = sqrt ( 9 * 9 ) = sqrt (9^2) = color(blue)(9$
$\sqrt{16} = \sqrt{2 \cdot 2 \cdot 2 \cdot 2} = \sqrt{4 \cdot 4} = \sqrt{4^{2}} = 4$ $sqrt (16) = sqrt (2 * 2 * 2 * 2 ) = sqrt ( 4 * 4 ) = sqrt (4^2) = color(blue)(4$

So, $\sqrt{\frac{81}{16}} = \frac{9}{4}$ $sqrt (81/16) = color(blue)(9/4$

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