Solve sqrt{8.32*4.68/2.1*1.001}

$$\sqrt { \frac { 8.32 \times 4.68 } { 2.1 \times 1.001 } }$$

Evaluate

$$\frac{16\sqrt{429}}{77}\approx 4.303857699$$

Solution Steps

Multiply 8.32 and 4.68 to get 38.9376.

$$\sqrt{\frac{38.9376}{2.1\times 1.001}}$$

Multiply 2.1 and 1.001 to get 2.1021.

$$\sqrt{\frac{38.9376}{2.1021}}$$

Expand \frac{38.9376}{2.1021} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{389376}{21021}}$$

Reduce the fraction \frac{389376}{21021} to lowest terms by extracting and canceling out 39.

$$\sqrt{\frac{9984}{539}}$$

Rewrite the square root of the division \sqrt{\frac{9984}{539}} as the division of square roots \frac{\sqrt{9984}}{\sqrt{539}}.

$$\frac{\sqrt{9984}}{\sqrt{539}}$$

Factor 9984=16^{2}\times 39. Rewrite the square root of the product \sqrt{16^{2}\times 39} as the product of square roots \sqrt{16^{2}}\sqrt{39}. Take the square root of 16^{2}.

$$\frac{16\sqrt{39}}{\sqrt{539}}$$

Factor 539=7^{2}\times 11. Rewrite the square root of the product \sqrt{7^{2}\times 11} as the product of square roots \sqrt{7^{2}}\sqrt{11}. Take the square root of 7^{2}.

$$\frac{16\sqrt{39}}{7\sqrt{11}}$$

Rationalize the denominator of \frac{16\sqrt{39}}{7\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$\frac{16\sqrt{39}\sqrt{11}}{7\left(\sqrt{11}\right)^{2}}$$

The square of \sqrt{11} is 11.

$$\frac{16\sqrt{39}\sqrt{11}}{7\times 11}$$

To multiply \sqrt{39} and \sqrt{11}, multiply the numbers under the square root.

$$\frac{16\sqrt{429}}{7\times 11}$$

Multiply 7 and 11 to get 77.

$$\frac{16\sqrt{429}}{77}$$