Solve 7sqrt{2}-8sqrt{18}+4sqrt{72}

$$7 \sqrt{ 2 } -8 \sqrt{ 18 } +4 \sqrt{ 72 }$$

Evaluate

$$7\sqrt{2}\approx 9.899494937$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$7\sqrt{2}-8\times 3\sqrt{2}+4\sqrt{72}$$

Multiply -8 and 3 to get -24.

$$7\sqrt{2}-24\sqrt{2}+4\sqrt{72}$$

Combine 7\sqrt{2} and -24\sqrt{2} to get -17\sqrt{2}.

$$-17\sqrt{2}+4\sqrt{72}$$

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}.

$$-17\sqrt{2}+4\times 6\sqrt{2}$$

Multiply 4 and 6 to get 24.

$$-17\sqrt{2}+24\sqrt{2}$$

Combine -17\sqrt{2} and 24\sqrt{2} to get 7\sqrt{2}.

$$7\sqrt{2}$$