Solve 752sqrt{2.6div8}

$$752 \sqrt{ 2.6 \div 8 }$$

Evaluate

$$\frac{188\sqrt{130}}{5}\approx 428.705959837$$

Solution Steps

Expand \frac{2.6}{8} by multiplying both numerator and the denominator by 10.

$$752\sqrt{\frac{26}{80}}$$

Reduce the fraction \frac{26}{80} to lowest terms by extracting and canceling out 2.

$$752\sqrt{\frac{13}{40}}$$

Rewrite the square root of the division \sqrt{\frac{13}{40}} as the division of square roots \frac{\sqrt{13}}{\sqrt{40}}.

$$752\times \frac{\sqrt{13}}{\sqrt{40}}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$752\times \frac{\sqrt{13}}{2\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{13}}{2\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$752\times \frac{\sqrt{13}\sqrt{10}}{2\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$752\times \frac{\sqrt{13}\sqrt{10}}{2\times 10}$$

To multiply \sqrt{13} and \sqrt{10}, multiply the numbers under the square root.

$$752\times \frac{\sqrt{130}}{2\times 10}$$

Multiply 2 and 10 to get 20.

$$752\times \frac{\sqrt{130}}{20}$$

Express 752\times \frac{\sqrt{130}}{20} as a single fraction.

$$\frac{752\sqrt{130}}{20}$$

Divide 752\sqrt{130} by 20 to get \frac{188}{5}\sqrt{130}.

$$\frac{188}{5}\sqrt{130}$$