Solve sqrt{10}*sqrt{5}-6/sqrt{2}

$$\sqrt { 10 } \times \sqrt { 5 } - \frac { 6 } { \sqrt { 2 } }$$

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

$$\sqrt{5}\sqrt{2}\sqrt{5}-\frac{6}{\sqrt{2}}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$5\sqrt{2}-\frac{6}{\sqrt{2}}$$

Rationalize the denominator of \frac{6}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$5\sqrt{2}-\frac{6\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$5\sqrt{2}-\frac{6\sqrt{2}}{2}$$

Divide 6\sqrt{2} by 2 to get 3\sqrt{2}.

$$5\sqrt{2}-3\sqrt{2}$$

Combine 5\sqrt{2} and -3\sqrt{2} to get 2\sqrt{2}.

$$2\sqrt{2}$$