Solve 4sqrt{8}+2sqrt{50}

$$4 \sqrt { 8 } + 2 \sqrt { 50 }$$

Evaluate

$$18\sqrt{2}\approx 25.455844123$$

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}.

$$4\times 2\sqrt{2}+2\sqrt{50}$$

Multiply 4 and 2 to get 8.

$$8\sqrt{2}+2\sqrt{50}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

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

Multiply 2 and 5 to get 10.

$$8\sqrt{2}+10\sqrt{2}$$

Combine 8\sqrt{2} and 10\sqrt{2} to get 18\sqrt{2}.

$$18\sqrt{2}$$