Solve 147sqrt{24div45}

$$147 \sqrt{ 24 \div 45 }$$

Evaluate

$$\frac{98\sqrt{30}}{5}\approx 107.353621271$$

Solution Steps

Reduce the fraction \frac{24}{45} to lowest terms by extracting and canceling out 3.

$$147\sqrt{\frac{8}{15}}$$

Rewrite the square root of the division \sqrt{\frac{8}{15}} as the division of square roots \frac{\sqrt{8}}{\sqrt{15}}.

$$147\times \frac{\sqrt{8}}{\sqrt{15}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$147\times \frac{2\sqrt{2}}{\sqrt{15}}$$

Rationalize the denominator of \frac{2\sqrt{2}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$147\times \frac{2\sqrt{2}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$147\times \frac{2\sqrt{2}\sqrt{15}}{15}$$

To multiply \sqrt{2} and \sqrt{15}, multiply the numbers under the square root.

$$147\times \frac{2\sqrt{30}}{15}$$

Express 147\times \frac{2\sqrt{30}}{15} as a single fraction.

$$\frac{147\times 2\sqrt{30}}{15}$$

Multiply 147 and 2 to get 294.

$$\frac{294\sqrt{30}}{15}$$

Divide 294\sqrt{30} by 15 to get \frac{98}{5}\sqrt{30}.

$$\frac{98}{5}\sqrt{30}$$