Solve sqrt{25/12}

$$\sqrt{ \frac{ 25 }{ 12 } }$$

Evaluate

$$\frac{5\sqrt{3}}{6}\approx 1.443375673$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{25}{12}} as the division of square roots \frac{\sqrt{25}}{\sqrt{12}}.

$$\frac{\sqrt{25}}{\sqrt{12}}$$

Calculate the square root of 25 and get 5.

$$\frac{5}{\sqrt{12}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

Rationalize the denominator of \frac{5}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{5\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{5\sqrt{3}}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{5\sqrt{3}}{6}$$