Solve sqrt{1+(20/13)^2-2*1*20/13*15/65}

$$\sqrt { 1 + ( \frac { 20 } { 13 } ) ^ { 2 } - 2 \times 1 \times \frac { 20 } { 13 } \times \frac { 15 } { 65 } }$$

Evaluate

$$\frac{\sqrt{449}}{13}\approx 1.629970777$$

Solution Steps

Calculate \frac{20}{13} to the power of 2 and get \frac{400}{169}.

$$\sqrt{1+\frac{400}{169}-2\times 1\times \frac{20}{13}\times \frac{15}{65}}$$

Convert 1 to fraction \frac{169}{169}.

$$\sqrt{\frac{169}{169}+\frac{400}{169}-2\times 1\times \frac{20}{13}\times \frac{15}{65}}$$

Since \frac{169}{169} and \frac{400}{169} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{169+400}{169}-2\times 1\times \frac{20}{13}\times \frac{15}{65}}$$

Add 169 and 400 to get 569.

$$\sqrt{\frac{569}{169}-2\times 1\times \frac{20}{13}\times \frac{15}{65}}$$

Multiply 2 and 1 to get 2.

$$\sqrt{\frac{569}{169}-2\times \frac{20}{13}\times \frac{15}{65}}$$

Express 2\times \frac{20}{13} as a single fraction.

$$\sqrt{\frac{569}{169}-\frac{2\times 20}{13}\times \frac{15}{65}}$$

Multiply 2 and 20 to get 40.

$$\sqrt{\frac{569}{169}-\frac{40}{13}\times \frac{15}{65}}$$

Reduce the fraction \frac{15}{65} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{569}{169}-\frac{40}{13}\times \frac{3}{13}}$$

Multiply \frac{40}{13} times \frac{3}{13} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{569}{169}-\frac{40\times 3}{13\times 13}}$$

Do the multiplications in the fraction \frac{40\times 3}{13\times 13}.

$$\sqrt{\frac{569}{169}-\frac{120}{169}}$$

Since \frac{569}{169} and \frac{120}{169} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{569-120}{169}}$$

Subtract 120 from 569 to get 449.

$$\sqrt{\frac{449}{169}}$$

Rewrite the square root of the division \sqrt{\frac{449}{169}} as the division of square roots \frac{\sqrt{449}}{\sqrt{169}}.

$$\frac{\sqrt{449}}{\sqrt{169}}$$

Calculate the square root of 169 and get 13.

$$\frac{\sqrt{449}}{13}$$