Solve 4sqrt{50}+5sqrt{2}

$$4 \sqrt { 50 } + 5 \sqrt { 2 }$$

Evaluate

$$25\sqrt{2}\approx 35.355339059$$

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}.

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

Multiply 4 and 5 to get 20.

$$20\sqrt{2}+5\sqrt{2}$$

Combine 20\sqrt{2} and 5\sqrt{2} to get 25\sqrt{2}.

$$25\sqrt{2}$$