Solve 15sqrt{32}+7sqrt{18}

$$15 \sqrt { 32 } + 7 \sqrt { 18 }$$

Evaluate

$$81\sqrt{2}\approx 114.551298552$$

Solution Steps

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$15\times 4\sqrt{2}+7\sqrt{18}$$

Multiply 15 and 4 to get 60.

$$60\sqrt{2}+7\sqrt{18}$$

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}.

$$60\sqrt{2}+7\times 3\sqrt{2}$$

Multiply 7 and 3 to get 21.

$$60\sqrt{2}+21\sqrt{2}$$

Combine 60\sqrt{2} and 21\sqrt{2} to get 81\sqrt{2}.

$$81\sqrt{2}$$