Solve 26325/252{frac{5/5sqrt{63}}}

$$\frac{ 26325 }{ \frac{ 252 }{ \frac{ 5 }{ 5 \sqrt{ 63 } } } }$$

Evaluate

$$\frac{975\sqrt{7}}{196}\approx 13.161262899$$

Solution Steps

Divide 26325 by \frac{252}{\frac{5}{5\sqrt{63}}} by multiplying 26325 by the reciprocal of \frac{252}{\frac{5}{5\sqrt{63}}}.

$$\frac{26325\times \frac{5}{5\sqrt{63}}}{252}$$

Factor 63=3^{2}\times 7. Rewrite the square root of the product \sqrt{3^{2}\times 7} as the product of square roots \sqrt{3^{2}}\sqrt{7}. Take the square root of 3^{2}.

$$\frac{26325\times \frac{5}{5\times 3\sqrt{7}}}{252}$$

Multiply 5 and 3 to get 15.

$$\frac{26325\times \frac{5}{15\sqrt{7}}}{252}$$

Rationalize the denominator of \frac{5}{15\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{26325\times \frac{5\sqrt{7}}{15\left(\sqrt{7}\right)^{2}}}{252}$$

The square of \sqrt{7} is 7.

$$\frac{26325\times \frac{5\sqrt{7}}{15\times 7}}{252}$$

Cancel out 5 in both numerator and denominator.

$$\frac{26325\times \frac{\sqrt{7}}{3\times 7}}{252}$$

Multiply 3 and 7 to get 21.

$$\frac{26325\times \frac{\sqrt{7}}{21}}{252}$$

Express 26325\times \frac{\sqrt{7}}{21} as a single fraction.

$$\frac{\frac{26325\sqrt{7}}{21}}{252}$$

Express \frac{\frac{26325\sqrt{7}}{21}}{252} as a single fraction.

$$\frac{26325\sqrt{7}}{21\times 252}$$

Cancel out 3\times 9 in both numerator and denominator.

$$\frac{975\sqrt{7}}{7\times 28}$$

Multiply 7 and 28 to get 196.

$$\frac{975\sqrt{7}}{196}$$