Solve 3sqrt{8}+4sqrt{8}

$$3 \sqrt { 8 } + 4 \sqrt { 8 }$$

Evaluate

$$14\sqrt{2}\approx 19.798989873$$

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}.

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

Multiply 3 and 2 to get 6.

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

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}.

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

Multiply 4 and 2 to get 8.

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

Combine 6\sqrt{2} and 8\sqrt{2} to get 14\sqrt{2}.

$$14\sqrt{2}$$