Solve sqrt{18}:quadsqrt{12}

$$\sqrt { 18 } : \quad \sqrt { 12 }$$

Evaluate

$$\frac{\sqrt{6}}{2}\approx 1.224744871$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{3\sqrt{2}}{\sqrt{12}}$$

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}.

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

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

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

The square of \sqrt{3} is 3.

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

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

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

Multiply 2 and 3 to get 6.

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

Divide 3\sqrt{6} by 6 to get \frac{1}{2}\sqrt{6}.

$$\frac{1}{2}\sqrt{6}$$