Solve 7sqrt{52*(28div655}

$$7 \sqrt{ 52 \times (28 \div 655 }$$

Evaluate

$$\frac{28\sqrt{59605}}{655}\approx 10.436576901$$

Solution Steps

Express 52\times \frac{28}{655} as a single fraction.

$$7\sqrt{\frac{52\times 28}{655}}$$

Multiply 52 and 28 to get 1456.

$$7\sqrt{\frac{1456}{655}}$$

Rewrite the square root of the division \sqrt{\frac{1456}{655}} as the division of square roots \frac{\sqrt{1456}}{\sqrt{655}}.

$$7\times \frac{\sqrt{1456}}{\sqrt{655}}$$

Factor 1456=4^{2}\times 91. Rewrite the square root of the product \sqrt{4^{2}\times 91} as the product of square roots \sqrt{4^{2}}\sqrt{91}. Take the square root of 4^{2}.

$$7\times \frac{4\sqrt{91}}{\sqrt{655}}$$

Rationalize the denominator of \frac{4\sqrt{91}}{\sqrt{655}} by multiplying numerator and denominator by \sqrt{655}.

$$7\times \frac{4\sqrt{91}\sqrt{655}}{\left(\sqrt{655}\right)^{2}}$$

The square of \sqrt{655} is 655.

$$7\times \frac{4\sqrt{91}\sqrt{655}}{655}$$

To multiply \sqrt{91} and \sqrt{655}, multiply the numbers under the square root.

$$7\times \frac{4\sqrt{59605}}{655}$$

Express 7\times \frac{4\sqrt{59605}}{655} as a single fraction.

$$\frac{7\times 4\sqrt{59605}}{655}$$

Multiply 7 and 4 to get 28.

$$\frac{28\sqrt{59605}}{655}$$