Solve sqrt{176}*sqrt{396}

$$\sqrt{ 176 } \times \sqrt{ 396 }$$

Evaluate

$$264$$

Solution Steps

Factor 176=4^{2}\times 11. Rewrite the square root of the product \sqrt{4^{2}\times 11} as the product of square roots \sqrt{4^{2}}\sqrt{11}. Take the square root of 4^{2}.

$$4\sqrt{11}\sqrt{396}$$

Factor 396=6^{2}\times 11. Rewrite the square root of the product \sqrt{6^{2}\times 11} as the product of square roots \sqrt{6^{2}}\sqrt{11}. Take the square root of 6^{2}.

$$4\sqrt{11}\times 6\sqrt{11}$$

Multiply 4 and 6 to get 24.

$$24\sqrt{11}\sqrt{11}$$

Multiply \sqrt{11} and \sqrt{11} to get 11.

$$24\times 11$$

Multiply 24 and 11 to get 264.

$$264$$

Factor

$$2^{3}\times 3\times 11$$