Solve sqrt{81*9div2}

$$\sqrt{ 81 \times 9 \div 2 }$$

Evaluate

$$\frac{27\sqrt{2}}{2}\approx 19.091883092$$

Solution Steps

Multiply 81 and 9 to get 729.

$$\sqrt{\frac{729}{2}}$$

Rewrite the square root of the division \sqrt{\frac{729}{2}} as the division of square roots \frac{\sqrt{729}}{\sqrt{2}}.

$$\frac{\sqrt{729}}{\sqrt{2}}$$

Calculate the square root of 729 and get 27.

$$\frac{27}{\sqrt{2}}$$

Rationalize the denominator of \frac{27}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{27\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{27\sqrt{2}}{2}$$