Solve -sqrt{27/64}

$$- \sqrt{ \frac{ 27 }{ 64 } }$$

Evaluate

$$-\frac{3\sqrt{3}}{8}\approx -0.649519053$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{27}{64}} as the division of square roots \frac{\sqrt{27}}{\sqrt{64}}.

$$-\frac{\sqrt{27}}{\sqrt{64}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$-\frac{3\sqrt{3}}{\sqrt{64}}$$

Calculate the square root of 64 and get 8.

$$-\frac{3\sqrt{3}}{8}$$