Solve 7sqrt{2}-3sqrt{8}+4sqrt{8}

$$7 \sqrt { 2 } - 3 \sqrt { 8 } + 4 \sqrt { 8 }$$

Evaluate

$$9\sqrt{2}\approx 12.727922061$$

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}.

$$7\sqrt{2}-3\times 2\sqrt{2}+4\sqrt{8}$$

Multiply -3 and 2 to get -6.

$$7\sqrt{2}-6\sqrt{2}+4\sqrt{8}$$

Combine 7\sqrt{2} and -6\sqrt{2} to get \sqrt{2}.

$$\sqrt{2}+4\sqrt{8}$$

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}.

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

Multiply 4 and 2 to get 8.

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

Combine \sqrt{2} and 8\sqrt{2} to get 9\sqrt{2}.

$$9\sqrt{2}$$