Solve 3sqrt{48}*sqrt{75}

$$3 \sqrt { 48 } \times \sqrt { 75 }$$

Evaluate

$$180$$

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}.

$$3\times 4\sqrt{3}\sqrt{75}$$

Multiply 3 and 4 to get 12.

$$12\sqrt{3}\sqrt{75}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$12\sqrt{3}\times 5\sqrt{3}$$

Multiply 12 and 5 to get 60.

$$60\sqrt{3}\sqrt{3}$$

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

$$60\times 3$$

Multiply 60 and 3 to get 180.

$$180$$

Factor

$$2^{2}\times 3^{2}\times 5$$