Solve frac{sqrt{1+sqrt{121}}}{sqrt{45+sqrt{900}}}=

$$\frac { \sqrt { 1 + \sqrt { 121 } } } { \sqrt { 45 + \sqrt { 900 } } } =$$

Evaluate

$$\frac{2}{5}=0.4$$

Solution Steps

Calculate the square root of 121 and get 11.

$$\frac{\sqrt{1+11}}{\sqrt{45+\sqrt{900}}}$$

Add 1 and 11 to get 12.

$$\frac{\sqrt{12}}{\sqrt{45+\sqrt{900}}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{2\sqrt{3}}{\sqrt{45+\sqrt{900}}}$$

Calculate the square root of 900 and get 30.

$$\frac{2\sqrt{3}}{\sqrt{45+30}}$$

Add 45 and 30 to get 75.

$$\frac{2\sqrt{3}}{\sqrt{75}}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$\frac{2\sqrt{3}}{5\sqrt{3}}$$

Cancel out \sqrt{3} in both numerator and denominator.

$$\frac{2}{5}$$

Factor

$$\frac{2}{5} = 0.4$$