Solve sqrt{8}(2sqrt{2}+3)

$$\sqrt { 8 } ( 2 \sqrt { 2 } + 3 )$$

Evaluate

$$6\sqrt{2}+8\approx 16.485281374$$

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}.

$$2\sqrt{2}\left(2\sqrt{2}+3\right)$$

Use the distributive property to multiply 2\sqrt{2} by 2\sqrt{2}+3.

$$4\left(\sqrt{2}\right)^{2}+6\sqrt{2}$$

The square of \sqrt{2} is 2.

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

Multiply 4 and 2 to get 8.

$$8+6\sqrt{2}$$