Solve sqrt{120}divsqrt{243}

$$\sqrt{ 120 } \div \sqrt{ 243 }$$

Evaluate

$$\frac{2\sqrt{10}}{9}\approx 0.702728369$$

Solution Steps

Factor 120=2^{2}\times 30. Rewrite the square root of the product \sqrt{2^{2}\times 30} as the product of square roots \sqrt{2^{2}}\sqrt{30}. Take the square root of 2^{2}.

$$\frac{2\sqrt{30}}{\sqrt{243}}$$

Factor 243=9^{2}\times 3. Rewrite the square root of the product \sqrt{9^{2}\times 3} as the product of square roots \sqrt{9^{2}}\sqrt{3}. Take the square root of 9^{2}.

$$\frac{2\sqrt{30}}{9\sqrt{3}}$$

Rationalize the denominator of \frac{2\sqrt{30}}{9\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{2\sqrt{30}\sqrt{3}}{9\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{2\sqrt{30}\sqrt{3}}{9\times 3}$$

Factor 30=3\times 10. Rewrite the square root of the product \sqrt{3\times 10} as the product of square roots \sqrt{3}\sqrt{10}.

$$\frac{2\sqrt{3}\sqrt{10}\sqrt{3}}{9\times 3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{2\times 3\sqrt{10}}{9\times 3}$$

Multiply 9 and 3 to get 27.

$$\frac{2\times 3\sqrt{10}}{27}$$

Multiply 2 and 3 to get 6.

$$\frac{6\sqrt{10}}{27}$$

Divide 6\sqrt{10} by 27 to get \frac{2}{9}\sqrt{10}.

$$\frac{2}{9}\sqrt{10}$$