Solve sqrt{8}(8sqrt{5}+2sqrt{7}-sqrt{2}+8)=

$$\sqrt { 8 } ( 8 \sqrt { 5 } + 2 \sqrt { 7 } - \sqrt { 2 } + 8 ) =$$

Evaluate

$$4\sqrt{14}+16\sqrt{2}+16\sqrt{10}-4\approx 84.190489108$$

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}.

$$2\sqrt{2}\left(8\sqrt{5}+2\sqrt{7}-\sqrt{2}+8\right)$$

Use the distributive property to multiply 2\sqrt{2} by 8\sqrt{5}+2\sqrt{7}-\sqrt{2}+8.

$$16\sqrt{2}\sqrt{5}+4\sqrt{2}\sqrt{7}-2\left(\sqrt{2}\right)^{2}+16\sqrt{2}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$16\sqrt{10}+4\sqrt{2}\sqrt{7}-2\left(\sqrt{2}\right)^{2}+16\sqrt{2}$$

To multiply \sqrt{2} and \sqrt{7}, multiply the numbers under the square root.

$$16\sqrt{10}+4\sqrt{14}-2\left(\sqrt{2}\right)^{2}+16\sqrt{2}$$

The square of \sqrt{2} is 2.

$$16\sqrt{10}+4\sqrt{14}-2\times 2+16\sqrt{2}$$

Multiply -2 and 2 to get -4.

$$16\sqrt{10}+4\sqrt{14}-4+16\sqrt{2}$$