Solve frac{20+10sqrt{2}}{1sqrt{10}}

$$\frac { 20 + 10 \sqrt { 2 } } { 1 \sqrt { 10 } }$$

Evaluate

$$2\sqrt{5}\left(\sqrt{2}+1\right)\approx 10.796691275$$

Solution Steps

Rationalize the denominator of \frac{20+10\sqrt{2}}{1\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\left(20+10\sqrt{2}\right)\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\left(20+10\sqrt{2}\right)\sqrt{10}}{10}$$

Use the distributive property to multiply 20+10\sqrt{2} by \sqrt{10}.

$$\frac{20\sqrt{10}+10\sqrt{2}\sqrt{10}}{10}$$

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

$$\frac{20\sqrt{10}+10\sqrt{2}\sqrt{2}\sqrt{5}}{10}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{20\sqrt{10}+10\times 2\sqrt{5}}{10}$$

Multiply 10 and 2 to get 20.

$$\frac{20\sqrt{10}+20\sqrt{5}}{10}$$

Factor

$$2 \sqrt{5} {(\sqrt{2} + 1)} = 10.796691275$$