Solve 3sqrt{27}*sqrt{48}

$$3 \sqrt { 27 } \times \sqrt { 48 }$$

Evaluate

$$108$$

Solution Steps

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$3\times 3\sqrt{3}\sqrt{48}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{3}\sqrt{48}$$

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}.

$$9\sqrt{3}\times 4\sqrt{3}$$

Multiply 9 and 4 to get 36.

$$36\sqrt{3}\sqrt{3}$$

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

$$36\times 3$$

Multiply 36 and 3 to get 108.

$$108$$

Factor

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