Solve 4sqrt{50}+3sqrt{18}

$$4 \sqrt { 50 } + 3 \sqrt { 18 }$$

Evaluate

$$29\sqrt{2}\approx 41.012193309$$

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}.

$$4\times 5\sqrt{2}+3\sqrt{18}$$

Multiply 4 and 5 to get 20.

$$20\sqrt{2}+3\sqrt{18}$$

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}.

$$20\sqrt{2}+3\times 3\sqrt{2}$$

Multiply 3 and 3 to get 9.

$$20\sqrt{2}+9\sqrt{2}$$

Combine 20\sqrt{2} and 9\sqrt{2} to get 29\sqrt{2}.

$$29\sqrt{2}$$