Solve frac{3sqrt{55}}{40}divsqrt{13}

$$\frac{ 3 \sqrt{ 55 } }{ 40 } \div \sqrt{ 13 }$$

Evaluate

$$\frac{3\sqrt{715}}{520}\approx 0.154266253$$

Solution Steps

Express \frac{\frac{3\sqrt{55}}{40}}{\sqrt{13}} as a single fraction.

$$\frac{3\sqrt{55}}{40\sqrt{13}}$$

Rationalize the denominator of \frac{3\sqrt{55}}{40\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{3\sqrt{55}\sqrt{13}}{40\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{3\sqrt{55}\sqrt{13}}{40\times 13}$$

To multiply \sqrt{55} and \sqrt{13}, multiply the numbers under the square root.

$$\frac{3\sqrt{715}}{40\times 13}$$

Multiply 40 and 13 to get 520.

$$\frac{3\sqrt{715}}{520}$$