Solve sqrt{72}-3sqrt{48}

$$\sqrt { 72 } - 3 \sqrt { 48 }$$

Evaluate

$$6\left(\sqrt{2}-2\sqrt{3}\right)\approx -12.299328317$$

Solution Steps

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$6\sqrt{2}-3\sqrt{48}$$

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}.

$$6\sqrt{2}-3\times 4\sqrt{3}$$

Multiply -3 and 4 to get -12.

$$6\sqrt{2}-12\sqrt{3}$$