Solve frac{10-sqrt{18}}{sqrt{2}}

$$\frac { 10 - \sqrt { 18 } } { \sqrt { 2 } }$$

Evaluate

$$5\sqrt{2}-3\approx 4.071067812$$

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}.

$$\frac{10-3\sqrt{2}}{\sqrt{2}}$$

Rationalize the denominator of \frac{10-3\sqrt{2}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\left(10-3\sqrt{2}\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\left(10-3\sqrt{2}\right)\sqrt{2}}{2}$$

Use the distributive property to multiply 10-3\sqrt{2} by \sqrt{2}.

$$\frac{10\sqrt{2}-3\left(\sqrt{2}\right)^{2}}{2}$$

The square of \sqrt{2} is 2.

$$\frac{10\sqrt{2}-3\times 2}{2}$$

Multiply -3 and 2 to get -6.

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

Divide each term of 10\sqrt{2}-6 by 2 to get 5\sqrt{2}-3.

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