Solve 6sqrt{72}+5sqrt{2}-5sqrt{18}

$$6 \sqrt { 72 } + 5 \sqrt { 2 } - 5 \sqrt { 18 }$$

Evaluate

$$26\sqrt{2}\approx 36.769552622$$

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}.

$$6\times 6\sqrt{2}+5\sqrt{2}-5\sqrt{18}$$

Multiply 6 and 6 to get 36.

$$36\sqrt{2}+5\sqrt{2}-5\sqrt{18}$$

Combine 36\sqrt{2} and 5\sqrt{2} to get 41\sqrt{2}.

$$41\sqrt{2}-5\sqrt{18}$$

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}.

$$41\sqrt{2}-5\times 3\sqrt{2}$$

Multiply -5 and 3 to get -15.

$$41\sqrt{2}-15\sqrt{2}$$

Combine 41\sqrt{2} and -15\sqrt{2} to get 26\sqrt{2}.

$$26\sqrt{2}$$