Solve sqrt{832*468/21*1001}

$$\sqrt { \frac { 832 \times 468 } { 21 \times 1001 } }$$

Evaluate

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

Solution Steps

Cancel out 3\times 13 in both numerator and denominator.

$$\sqrt{\frac{64\times 156}{7\times 77}}$$

Multiply 64 and 156 to get 9984.

$$\sqrt{\frac{9984}{7\times 77}}$$

Multiply 7 and 77 to get 539.

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

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.

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