Solve frac{sqrt{1000}}{sqrt{910}}

$$\frac { \sqrt { 1000 } } { \sqrt { 910 } }$$

Evaluate

$$\frac{10\sqrt{91}}{91}\approx 1.048284837$$

Solution Steps

Factor 1000=10^{2}\times 10. Rewrite the square root of the product \sqrt{10^{2}\times 10} as the product of square roots \sqrt{10^{2}}\sqrt{10}. Take the square root of 10^{2}.

$$\frac{10\sqrt{10}}{\sqrt{910}}$$

Rationalize the denominator of \frac{10\sqrt{10}}{\sqrt{910}} by multiplying numerator and denominator by \sqrt{910}.

$$\frac{10\sqrt{10}\sqrt{910}}{\left(\sqrt{910}\right)^{2}}$$

The square of \sqrt{910} is 910.

$$\frac{10\sqrt{10}\sqrt{910}}{910}$$

Factor 910=10\times 91. Rewrite the square root of the product \sqrt{10\times 91} as the product of square roots \sqrt{10}\sqrt{91}.

$$\frac{10\sqrt{10}\sqrt{10}\sqrt{91}}{910}$$

Multiply \sqrt{10} and \sqrt{10} to get 10.

$$\frac{10\times 10\sqrt{91}}{910}$$

Multiply 10 and 10 to get 100.

$$\frac{100\sqrt{91}}{910}$$

Divide 100\sqrt{91} by 910 to get \frac{10}{91}\sqrt{91}.

$$\frac{10}{91}\sqrt{91}$$