Solve sqrt{(35/26)^2+(161/78)^2}

$$\sqrt { ( \frac { 35 } { 26 } ) ^ { 2 } + ( \frac { 161 } { 78 } ) ^ { 2 } }$$

Evaluate

$$\frac{7\sqrt{754}}{78}\approx 2.464274654$$

Solution Steps

Calculate \frac{35}{26} to the power of 2 and get \frac{1225}{676}.

$$\sqrt{\frac{1225}{676}+\left(\frac{161}{78}\right)^{2}}$$

Calculate \frac{161}{78} to the power of 2 and get \frac{25921}{6084}.

$$\sqrt{\frac{1225}{676}+\frac{25921}{6084}}$$

Least common multiple of 676 and 6084 is 6084. Convert \frac{1225}{676} and \frac{25921}{6084} to fractions with denominator 6084.

$$\sqrt{\frac{11025}{6084}+\frac{25921}{6084}}$$

Since \frac{11025}{6084} and \frac{25921}{6084} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{11025+25921}{6084}}$$

Add 11025 and 25921 to get 36946.

$$\sqrt{\frac{36946}{6084}}$$

Reduce the fraction \frac{36946}{6084} to lowest terms by extracting and canceling out 26.

$$\sqrt{\frac{1421}{234}}$$

Rewrite the square root of the division \sqrt{\frac{1421}{234}} as the division of square roots \frac{\sqrt{1421}}{\sqrt{234}}.

$$\frac{\sqrt{1421}}{\sqrt{234}}$$

Factor 1421=7^{2}\times 29. Rewrite the square root of the product \sqrt{7^{2}\times 29} as the product of square roots \sqrt{7^{2}}\sqrt{29}. Take the square root of 7^{2}.

$$\frac{7\sqrt{29}}{\sqrt{234}}$$

Factor 234=3^{2}\times 26. Rewrite the square root of the product \sqrt{3^{2}\times 26} as the product of square roots \sqrt{3^{2}}\sqrt{26}. Take the square root of 3^{2}.

$$\frac{7\sqrt{29}}{3\sqrt{26}}$$

Rationalize the denominator of \frac{7\sqrt{29}}{3\sqrt{26}} by multiplying numerator and denominator by \sqrt{26}.

$$\frac{7\sqrt{29}\sqrt{26}}{3\left(\sqrt{26}\right)^{2}}$$

The square of \sqrt{26} is 26.

$$\frac{7\sqrt{29}\sqrt{26}}{3\times 26}$$

To multiply \sqrt{29} and \sqrt{26}, multiply the numbers under the square root.

$$\frac{7\sqrt{754}}{3\times 26}$$

Multiply 3 and 26 to get 78.

$$\frac{7\sqrt{754}}{78}$$