How do you simplify $\sqrt{\frac{3}{27 y^{6}}}$ $sqrt(3/(27y^6))$ ?

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Answer 1 · 2015-09-25T01:52:53

$\sqrt{\frac{3}{27 y^{6}}} = \frac{1}{3 y^{3}}$ $color(red)(sqrt(3/(27y^6))= 1/(3y^3))$

First divide the numerator and denominator by $3$ $3$ .

$\sqrt{\frac{3}{27 y^{6}}} = \sqrt{\frac{1}{9 y^{6}}}$ $sqrt(3/(27y^6)) = sqrt(1/(9y^6))$

Remember that $\sqrt{x^{n}} = x^{\frac{n}{2}}$ $sqrt(x^n) = x^(n/2)$

So $\sqrt{y^{6}} = y^{\frac{6}{2}} = y^{3}$ $sqrt(y^6) = y^(6/2) = y^3$ and

$\sqrt{\frac{1}{9 y^{6}}} = \frac{1}{3 y^{3}}$ $sqrt(1/(9y^6)) = 1/(3y^3)$

∴ $\sqrt{\frac{3}{27 y^{6}}} = \frac{1}{3 y^{3}}$ $sqrt(3/(27y^6))= 1/(3y^3)$

How do you simplify sqrt(3/(27y^6))√327y6sqrt(3/(27y^6))?