Solve sqrt{41/2}

$$\sqrt { 4 \frac { 1 } { 2 } }$$

Evaluate

$$\frac{3\sqrt{2}}{2}\approx 2.121320344$$

Solution Steps

Multiply 4 and 2 to get 8.

$$\sqrt{\frac{8+1}{2}}$$

Add 8 and 1 to get 9.

$$\sqrt{\frac{9}{2}}$$

Rewrite the square root of the division \sqrt{\frac{9}{2}} as the division of square roots \frac{\sqrt{9}}{\sqrt{2}}.

$$\frac{\sqrt{9}}{\sqrt{2}}$$

Calculate the square root of 9 and get 3.

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

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

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

The square of \sqrt{2} is 2.

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