Solve 5sqrt{2}+7sqrt{8}

$$5 \sqrt { 2 } + 7 \sqrt { 8 }$$

Evaluate

$$19\sqrt{2}\approx 26.870057685$$

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}.

$$5\sqrt{2}+7\times 2\sqrt{2}$$

Multiply 7 and 2 to get 14.

$$5\sqrt{2}+14\sqrt{2}$$

Combine 5\sqrt{2} and 14\sqrt{2} to get 19\sqrt{2}.

$$19\sqrt{2}$$