Solve sqrt{2}divsqrt{12}-1

$$\sqrt { 2 } \div \sqrt { 12 } - 1$$

Evaluate

$$\frac{\sqrt{6}}{6}-1\approx -0.59175171$$

Solution Steps

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}.

$$\frac{\sqrt{2}}{2\sqrt{3}}-1$$

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

$$\frac{\sqrt{2}\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}-1$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{2}\sqrt{3}}{2\times 3}-1$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{2\times 3}-1$$

Multiply 2 and 3 to get 6.

$$\frac{\sqrt{6}}{6}-1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{6}{6}.

$$\frac{\sqrt{6}}{6}-\frac{6}{6}$$

Since \frac{\sqrt{6}}{6} and \frac{6}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\sqrt{6}-6}{6}$$