Solve frac{12+9sqrt{2}}{sqrt{2}}*frac{sqrt{2}}{sqrt{2}}=

$$\frac { 12 + 9 \sqrt { 2 } } { \sqrt { 2 } } \times \frac { \sqrt { 2 } } { \sqrt { 2 } } =$$

Evaluate

$$3\left(2\sqrt{2}+3\right)\approx 17.485281374$$

Solution Steps

Divide \sqrt{2} by \sqrt{2} to get 1.

$$\frac{12+9\sqrt{2}}{\sqrt{2}}\times 1$$

Rationalize the denominator of \frac{12+9\sqrt{2}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\left(12+9\sqrt{2}\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\times 1$$

The square of \sqrt{2} is 2.

$$\frac{\left(12+9\sqrt{2}\right)\sqrt{2}}{2}\times 1$$

Express \frac{\left(12+9\sqrt{2}\right)\sqrt{2}}{2}\times 1 as a single fraction.

$$\frac{\left(12+9\sqrt{2}\right)\sqrt{2}}{2}$$

Use the distributive property to multiply 12+9\sqrt{2} by \sqrt{2}.

$$\frac{12\sqrt{2}+9\left(\sqrt{2}\right)^{2}}{2}$$

The square of \sqrt{2} is 2.

$$\frac{12\sqrt{2}+9\times 2}{2}$$

Multiply 9 and 2 to get 18.

$$\frac{12\sqrt{2}+18}{2}$$

Factor

$$3 {(2 \sqrt{2} + 3)} = 17.485281374$$