Solve (sqrt{32}+sqrt{18}*sqrt{2}

$$( \sqrt { 32 } + \sqrt { 18 } \times \sqrt { 2 }$$

Evaluate

$$2^{\frac{5}{2}}+6\approx 11.656854249$$

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}.

$$4\sqrt{2}+\sqrt{18}\sqrt{2}$$

Factor 18=2\times 9. Rewrite the square root of the product \sqrt{2\times 9} as the product of square roots \sqrt{2}\sqrt{9}.

$$4\sqrt{2}+\sqrt{2}\sqrt{9}\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$4\sqrt{2}+2\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$4\sqrt{2}+2\times 3$$

Multiply 2 and 3 to get 6.

$$4\sqrt{2}+6$$