Solve |-2|/sqrt{75}

$$\frac { | - 2 | } { \sqrt { 75 } }$$

Evaluate

$$\frac{2\sqrt{3}}{15}\approx 0.230940108$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -2 is 2.

$$\frac{2}{\sqrt{75}}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

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

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

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

The square of \sqrt{3} is 3.

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

Multiply 5 and 3 to get 15.

$$\frac{2\sqrt{3}}{15}$$