Solve sqrt{3*9*13*10^-3}

$$\sqrt{ 3 \cdot 9 \cdot 13 \times { 10 }^{ -3 } }$$

Evaluate

$$\frac{3\sqrt{390}}{100}\approx 0.59245253$$

Solution Steps

Multiply 3 and 9 to get 27.

$$\sqrt{27\times 13\times 10^{-3}}$$

Multiply 27 and 13 to get 351.

$$\sqrt{351\times 10^{-3}}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\sqrt{351\times \frac{1}{1000}}$$

Multiply 351 and \frac{1}{1000} to get \frac{351}{1000}.

$$\sqrt{\frac{351}{1000}}$$

Rewrite the square root of the division \sqrt{\frac{351}{1000}} as the division of square roots \frac{\sqrt{351}}{\sqrt{1000}}.

$$\frac{\sqrt{351}}{\sqrt{1000}}$$

Factor 351=3^{2}\times 39. Rewrite the square root of the product \sqrt{3^{2}\times 39} as the product of square roots \sqrt{3^{2}}\sqrt{39}. Take the square root of 3^{2}.

$$\frac{3\sqrt{39}}{\sqrt{1000}}$$

Factor 1000=10^{2}\times 10. Rewrite the square root of the product \sqrt{10^{2}\times 10} as the product of square roots \sqrt{10^{2}}\sqrt{10}. Take the square root of 10^{2}.

$$\frac{3\sqrt{39}}{10\sqrt{10}}$$

Rationalize the denominator of \frac{3\sqrt{39}}{10\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{3\sqrt{39}\sqrt{10}}{10\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{3\sqrt{39}\sqrt{10}}{10\times 10}$$

To multiply \sqrt{39} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{3\sqrt{390}}{10\times 10}$$

Multiply 10 and 10 to get 100.

$$\frac{3\sqrt{390}}{100}$$