Solve sqrt{63}*sqrt{448}

$$\sqrt { 63 } \cdot \sqrt { 448 }$$

Evaluate

$$168$$

Solution Steps

Factor 63=3^{2}\times 7. Rewrite the square root of the product \sqrt{3^{2}\times 7} as the product of square roots \sqrt{3^{2}}\sqrt{7}. Take the square root of 3^{2}.

$$3\sqrt{7}\sqrt{448}$$

Factor 448=8^{2}\times 7. Rewrite the square root of the product \sqrt{8^{2}\times 7} as the product of square roots \sqrt{8^{2}}\sqrt{7}. Take the square root of 8^{2}.

$$3\sqrt{7}\times 8\sqrt{7}$$

Multiply 3 and 8 to get 24.

$$24\sqrt{7}\sqrt{7}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$24\times 7$$

Multiply 24 and 7 to get 168.

$$168$$

Factor

$$2^{3}\times 3\times 7$$