Solve sqrt{left(18div13right)^2+left(12div13right)^22}

$$\sqrt{ { \left(18 \div 13 \right) }^{ 2 } + { \left(12 \div 13 \right) }^{ 22 } }$$

Evaluate

$$\frac{18\sqrt{20708857104857455048657}}{1792160394037}\approx 1.445352225$$

Solution Steps

Calculate \frac{18}{13} to the power of 2 and get \frac{324}{169}.

$$\sqrt{\frac{324}{169}+\left(\frac{12}{13}\right)^{22}}$$

Calculate \frac{12}{13} to the power of 22 and get \frac{552061438912436417593344}{3211838877954855105157369}.

$$\sqrt{\frac{324}{169}+\frac{552061438912436417593344}{3211838877954855105157369}}$$

Least common multiple of 169 and 3211838877954855105157369 is 3211838877954855105157369. Convert \frac{324}{169} and \frac{552061438912436417593344}{3211838877954855105157369} to fractions with denominator 3211838877954855105157369.

$$\sqrt{\frac{6157608263061379018171524}{3211838877954855105157369}+\frac{552061438912436417593344}{3211838877954855105157369}}$$

Since \frac{6157608263061379018171524}{3211838877954855105157369} and \frac{552061438912436417593344}{3211838877954855105157369} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{6157608263061379018171524+552061438912436417593344}{3211838877954855105157369}}$$

Add 6157608263061379018171524 and 552061438912436417593344 to get 6709669701973815435764868.

$$\sqrt{\frac{6709669701973815435764868}{3211838877954855105157369}}$$

Rewrite the square root of the division \sqrt{\frac{6709669701973815435764868}{3211838877954855105157369}} as the division of square roots \frac{\sqrt{6709669701973815435764868}}{\sqrt{3211838877954855105157369}}.

$$\frac{\sqrt{6709669701973815435764868}}{\sqrt{3211838877954855105157369}}$$

Factor 6709669701973815435764868=18^{2}\times 20708857104857455048657. Rewrite the square root of the product \sqrt{18^{2}\times 20708857104857455048657} as the product of square roots \sqrt{18^{2}}\sqrt{20708857104857455048657}. Take the square root of 18^{2}.

$$\frac{18\sqrt{20708857104857455048657}}{\sqrt{3211838877954855105157369}}$$

Calculate the square root of 3211838877954855105157369 and get 1792160394037.

$$\frac{18\sqrt{20708857104857455048657}}{1792160394037}$$