Solve sqrt{48}*sqrt{108}

$$\sqrt { 48 } \times \sqrt { 108 }$$

Evaluate

$$72$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$4\sqrt{3}\sqrt{108}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$4\sqrt{3}\times 6\sqrt{3}$$

Multiply 4 and 6 to get 24.

$$24\sqrt{3}\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$24\times 3$$

Multiply 24 and 3 to get 72.

$$72$$

Factor

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