Solve sqrt{27*10^-2}

$$\sqrt { 27 \times 10 ^ { - 2 } }$$

Evaluate

$$\frac{3\sqrt{3}}{10}\approx 0.519615242$$

Solution Steps

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\sqrt{27\times \frac{1}{100}}$$

Multiply 27 and \frac{1}{100} to get \frac{27}{100}.

$$\sqrt{\frac{27}{100}}$$

Rewrite the square root of the division \sqrt{\frac{27}{100}} as the division of square roots \frac{\sqrt{27}}{\sqrt{100}}.

$$\frac{\sqrt{27}}{\sqrt{100}}$$

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}.

$$\frac{3\sqrt{3}}{\sqrt{100}}$$

Calculate the square root of 100 and get 10.

$$\frac{3\sqrt{3}}{10}$$