Solve sqrt{16+8+16sqrt{2}*(-frac{sqrt{2}}{2})}

$$\sqrt{ 16+8+16 \sqrt{ 2 } \times (- \frac{ \sqrt{ 2 } }{ 2 } ) }$$

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

Add 16 and 8 to get 24.

$$\sqrt{24+16\sqrt{2}\left(-\frac{\sqrt{2}}{2}\right)}$$

Cancel out 2, the greatest common factor in 16 and 2.

$$\sqrt{24-8\sqrt{2}\sqrt{2}}$$

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

$$\sqrt{24-8\times 2}$$

Multiply -8 and 2 to get -16.

$$\sqrt{24-16}$$

Subtract 16 from 24 to get 8.

$$\sqrt{8}$$

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}.

$$2\sqrt{2}$$