Solve -4sqrt{18}+6sqrt{200}

$$- 4 \sqrt { 18 } + 6 \sqrt { 200 }$$

Evaluate

$$48\sqrt{2}\approx 67.882250994$$

Solution Steps

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}.

$$-4\times 3\sqrt{2}+6\sqrt{200}$$

Multiply -4 and 3 to get -12.

$$-12\sqrt{2}+6\sqrt{200}$$

Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.

$$-12\sqrt{2}+6\times 10\sqrt{2}$$

Multiply 6 and 10 to get 60.

$$-12\sqrt{2}+60\sqrt{2}$$

Combine -12\sqrt{2} and 60\sqrt{2} to get 48\sqrt{2}.

$$48\sqrt{2}$$