Solve sqrt{40}:sqrt{15}

$$\sqrt { 40 } : \sqrt { 15 }$$

Evaluate

$$\frac{2\sqrt{6}}{3}\approx 1.632993162$$

Solution Steps

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\frac{2\sqrt{10}}{\sqrt{15}}$$

Rationalize the denominator of \frac{2\sqrt{10}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{2\sqrt{10}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{2\sqrt{10}\sqrt{15}}{15}$$

To multiply \sqrt{10} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{2\sqrt{150}}{15}$$

Factor 150=5^{2}\times 6. Rewrite the square root of the product \sqrt{5^{2}\times 6} as the product of square roots \sqrt{5^{2}}\sqrt{6}. Take the square root of 5^{2}.

$$\frac{2\times 5\sqrt{6}}{15}$$

Multiply 2 and 5 to get 10.

$$\frac{10\sqrt{6}}{15}$$

Divide 10\sqrt{6} by 15 to get \frac{2}{3}\sqrt{6}.

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