Solve 4sqrt{2}+3sqrt{50}

$$4 \sqrt { 2 } + 3 \sqrt { 50 }$$

Evaluate

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

Solution Steps

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}.

$$4\sqrt{2}+3\times 5\sqrt{2}$$

Multiply 3 and 5 to get 15.

$$4\sqrt{2}+15\sqrt{2}$$

Combine 4\sqrt{2} and 15\sqrt{2} to get 19\sqrt{2}.

$$19\sqrt{2}$$