Solve frac{4sqrt{625}}{7sqrt{7}}

$$\frac { 4 \sqrt { 625 } } { 7 \sqrt { 7 } }$$

Evaluate

$$\frac{100\sqrt{7}}{49}\approx 5.399492472$$

Solution Steps

Calculate the square root of 625 and get 25.

$$\frac{4\times 25}{7\sqrt{7}}$$

Multiply 4 and 25 to get 100.

$$\frac{100}{7\sqrt{7}}$$

Rationalize the denominator of \frac{100}{7\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{100\sqrt{7}}{7\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{100\sqrt{7}}{7\times 7}$$

Multiply 7 and 7 to get 49.

$$\frac{100\sqrt{7}}{49}$$