Solve y10/sqrt{2}-frac{sqrt{8}}{2}

$$y \frac { 10 } { \sqrt { 2 } } - \frac { \sqrt { 8 } } { 2 }$$

Evaluate

$$\sqrt{2}\left(5y-1\right)$$

Solution Steps

Rationalize the denominator of \frac{10}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$y\times \frac{10\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\frac{\sqrt{8}}{2}$$

The square of \sqrt{2} is 2.

$$y\times \frac{10\sqrt{2}}{2}-\frac{\sqrt{8}}{2}$$

Divide 10\sqrt{2} by 2 to get 5\sqrt{2}.

$$y\times 5\sqrt{2}-\frac{\sqrt{8}}{2}$$

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}.

$$y\times 5\sqrt{2}-\frac{2\sqrt{2}}{2}$$

Cancel out 2 and 2.

$$y\times 5\sqrt{2}-\sqrt{2}$$

Factor

$$\sqrt{2}\left(5y-1\right)$$

Solution Steps

Rationalize the denominator of \frac{10}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$factor(y\times \frac{10\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\frac{\sqrt{8}}{2})$$

The square of \sqrt{2} is 2.

$$factor(y\times \frac{10\sqrt{2}}{2}-\frac{\sqrt{8}}{2})$$

Divide 10\sqrt{2} by 2 to get 5\sqrt{2}.

$$factor(y\times 5\sqrt{2}-\frac{\sqrt{8}}{2})$$

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}.

$$factor(y\times 5\sqrt{2}-\frac{2\sqrt{2}}{2})$$

Cancel out 2 and 2.

$$factor(y\times 5\sqrt{2}-\sqrt{2})$$

Factor out \sqrt{2}.

$$\sqrt{2}\left(5y-1\right)$$