Solve 3/7sqrt{103/9}

$$\frac { 3 } { 7 } \sqrt { 10 \frac { 3 } { 9 } }$$

Evaluate

$$\frac{\sqrt{93}}{7}\approx 1.377664394$$

Solution Steps

Multiply 10 and 9 to get 90.

$$\frac{3}{7}\sqrt{\frac{90+3}{9}}$$

Add 90 and 3 to get 93.

$$\frac{3}{7}\sqrt{\frac{93}{9}}$$

Reduce the fraction \frac{93}{9} to lowest terms by extracting and canceling out 3.

$$\frac{3}{7}\sqrt{\frac{31}{3}}$$

Rewrite the square root of the division \sqrt{\frac{31}{3}} as the division of square roots \frac{\sqrt{31}}{\sqrt{3}}.

$$\frac{3}{7}\times \frac{\sqrt{31}}{\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{31}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{3}{7}\times \frac{\sqrt{31}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{3}{7}\times \frac{\sqrt{31}\sqrt{3}}{3}$$

To multiply \sqrt{31} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{3}{7}\times \frac{\sqrt{93}}{3}$$

Multiply \frac{3}{7} times \frac{\sqrt{93}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\sqrt{93}}{7\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\sqrt{93}}{7}$$