Solve sqrt{{left(6/11right)}^22+{left(7/11right)}^2}

$$\sqrt{ { \left( \frac{ 6 }{ 11 } \right) }^{ 2 } 2+ { \left( \frac{ 7 }{ 11 } \right) }^{ 2 } }$$

Evaluate

$$1$$

Solution Steps

Calculate \frac{6}{11} to the power of 2 and get \frac{36}{121}.

$$\sqrt{\frac{36}{121}\times 2+\left(\frac{7}{11}\right)^{2}}$$

Express \frac{36}{121}\times 2 as a single fraction.

$$\sqrt{\frac{36\times 2}{121}+\left(\frac{7}{11}\right)^{2}}$$

Multiply 36 and 2 to get 72.

$$\sqrt{\frac{72}{121}+\left(\frac{7}{11}\right)^{2}}$$

Calculate \frac{7}{11} to the power of 2 and get \frac{49}{121}.

$$\sqrt{\frac{72}{121}+\frac{49}{121}}$$

Since \frac{72}{121} and \frac{49}{121} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{72+49}{121}}$$

Add 72 and 49 to get 121.

$$\sqrt{\frac{121}{121}}$$

Divide 121 by 121 to get 1.

$$\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$1$$

Factor

$$1$$