Solve frac{-10sqrt{2}-sqrt{200}+400sqrt{2}}{5sqrt{2}}

$$\frac { - 10 \sqrt { 2 } - \sqrt { 200 } + 400 \sqrt { 2 } } { 5 \sqrt { 2 } }$$

Evaluate

$$76$$

Solution Steps

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}.

$$\frac{-10\sqrt{2}-10\sqrt{2}+400\sqrt{2}}{5\sqrt{2}}$$

Combine -10\sqrt{2} and -10\sqrt{2} to get -20\sqrt{2}.

$$\frac{-20\sqrt{2}+400\sqrt{2}}{5\sqrt{2}}$$

Combine -20\sqrt{2} and 400\sqrt{2} to get 380\sqrt{2}.

$$\frac{380\sqrt{2}}{5\sqrt{2}}$$

Cancel out 5\sqrt{2} in both numerator and denominator.

$$76$$

Factor

$$2^{2}\times 19$$