Solve sqrt{135}divsqrt{80}

$$\sqrt{ 135 } \div \sqrt{ 80 }$$

Evaluate

$$\frac{3\sqrt{3}}{4}\approx 1.299038106$$

Solution Steps

Factor 135=3^{2}\times 15. Rewrite the square root of the product \sqrt{3^{2}\times 15} as the product of square roots \sqrt{3^{2}}\sqrt{15}. Take the square root of 3^{2}.

$$\frac{3\sqrt{15}}{\sqrt{80}}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$\frac{3\sqrt{15}}{4\sqrt{5}}$$

Rationalize the denominator of \frac{3\sqrt{15}}{4\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{3\sqrt{15}\sqrt{5}}{4\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{3\sqrt{15}\sqrt{5}}{4\times 5}$$

Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.

$$\frac{3\sqrt{5}\sqrt{3}\sqrt{5}}{4\times 5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{3\times 5\sqrt{3}}{4\times 5}$$

Multiply 4 and 5 to get 20.

$$\frac{3\times 5\sqrt{3}}{20}$$

Multiply 3 and 5 to get 15.

$$\frac{15\sqrt{3}}{20}$$

Divide 15\sqrt{3} by 20 to get \frac{3}{4}\sqrt{3}.

$$\frac{3}{4}\sqrt{3}$$