Solve (sqrt{50}+sqrt{32}-sqrt{3}*sqrt{6})divsqrt{8}

$$( \sqrt { 50 } + \sqrt { 32 } - \sqrt { 3 } \times \sqrt { 6 } ) \div \sqrt { 8 }$$

Evaluate

$$3$$

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}.

$$\frac{5\sqrt{2}+\sqrt{32}-\sqrt{3}\sqrt{6}}{\sqrt{8}}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\frac{5\sqrt{2}+4\sqrt{2}-\sqrt{3}\sqrt{6}}{\sqrt{8}}$$

Combine 5\sqrt{2} and 4\sqrt{2} to get 9\sqrt{2}.

$$\frac{9\sqrt{2}-\sqrt{3}\sqrt{6}}{\sqrt{8}}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$\frac{9\sqrt{2}-\sqrt{3}\sqrt{3}\sqrt{2}}{\sqrt{8}}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{9\sqrt{2}-3\sqrt{2}}{\sqrt{8}}$$

Combine 9\sqrt{2} and -3\sqrt{2} to get 6\sqrt{2}.

$$\frac{6\sqrt{2}}{\sqrt{8}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{6\sqrt{2}}{2\sqrt{2}}$$

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

$$3$$

Factor

$$3$$