Solve 3sqrt{50}+5sqrt{18}

$$3 \sqrt { 50 } + 5 \sqrt { 18 }$$

Evaluate

$$30\sqrt{2}\approx 42.426406871$$

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}.

$$3\times 5\sqrt{2}+5\sqrt{18}$$

Multiply 3 and 5 to get 15.

$$15\sqrt{2}+5\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$15\sqrt{2}+5\times 3\sqrt{2}$$

Multiply 5 and 3 to get 15.

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

Combine 15\sqrt{2} and 15\sqrt{2} to get 30\sqrt{2}.

$$30\sqrt{2}$$