Solve 5sqrt{8}-3sqrt{72}

$$5 \sqrt { 8 } - 3 \sqrt { 72 }$$

Evaluate

$$-8\sqrt{2}\approx -11.313708499$$

Solution Steps

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

$$5\times 2\sqrt{2}-3\sqrt{72}$$

Multiply 5 and 2 to get 10.

$$10\sqrt{2}-3\sqrt{72}$$

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}.

$$10\sqrt{2}-3\times 6\sqrt{2}$$

Multiply -3 and 6 to get -18.

$$10\sqrt{2}-18\sqrt{2}$$

Combine 10\sqrt{2} and -18\sqrt{2} to get -8\sqrt{2}.

$$-8\sqrt{2}$$