Solve sqrt{frac{1^{3}+3^{3}+5^{3}+7^{3}+9^{3}}{1^{3}+2^{3}+3^3+4^3+5^3+6^3}}

$$\sqrt { \frac { 1 ^ { 3 } + 3 ^ { 3 } + 5 ^ { 3 } + 7 ^ { 3 } + 9 ^ { 3 } } { 1 ^ { 3 } + 2 ^ { 3 } + 3 ^ { 3 } + 4 ^ { 3 } + 5 ^ { 3 } + 6 ^ { 3 } } }$$

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

Solution Steps

Calculate 1 to the power of 3 and get 1.

$$\sqrt{\frac{1+3^{3}+5^{3}+7^{3}+9^{3}}{1^{3}+2^{3}+3^{3}+4^{3}+5^{3}+6^{3}}}$$

Calculate 3 to the power of 3 and get 27.

$$\sqrt{\frac{1+27+5^{3}+7^{3}+9^{3}}{1^{3}+2^{3}+3^{3}+4^{3}+5^{3}+6^{3}}}$$

Add 1 and 27 to get 28.

$$\sqrt{\frac{28+5^{3}+7^{3}+9^{3}}{1^{3}+2^{3}+3^{3}+4^{3}+5^{3}+6^{3}}}$$

Calculate 5 to the power of 3 and get 125.

$$\sqrt{\frac{28+125+7^{3}+9^{3}}{1^{3}+2^{3}+3^{3}+4^{3}+5^{3}+6^{3}}}$$

Add 28 and 125 to get 153.

$$\sqrt{\frac{153+7^{3}+9^{3}}{1^{3}+2^{3}+3^{3}+4^{3}+5^{3}+6^{3}}}$$

Calculate 7 to the power of 3 and get 343.

$$\sqrt{\frac{153+343+9^{3}}{1^{3}+2^{3}+3^{3}+4^{3}+5^{3}+6^{3}}}$$

Add 153 and 343 to get 496.

$$\sqrt{\frac{496+9^{3}}{1^{3}+2^{3}+3^{3}+4^{3}+5^{3}+6^{3}}}$$

Calculate 9 to the power of 3 and get 729.

$$\sqrt{\frac{496+729}{1^{3}+2^{3}+3^{3}+4^{3}+5^{3}+6^{3}}}$$

Add 496 and 729 to get 1225.

$$\sqrt{\frac{1225}{1^{3}+2^{3}+3^{3}+4^{3}+5^{3}+6^{3}}}$$

Calculate 1 to the power of 3 and get 1.

$$\sqrt{\frac{1225}{1+2^{3}+3^{3}+4^{3}+5^{3}+6^{3}}}$$

Calculate 2 to the power of 3 and get 8.

$$\sqrt{\frac{1225}{1+8+3^{3}+4^{3}+5^{3}+6^{3}}}$$

Add 1 and 8 to get 9.

$$\sqrt{\frac{1225}{9+3^{3}+4^{3}+5^{3}+6^{3}}}$$

Calculate 3 to the power of 3 and get 27.

$$\sqrt{\frac{1225}{9+27+4^{3}+5^{3}+6^{3}}}$$

Add 9 and 27 to get 36.

$$\sqrt{\frac{1225}{36+4^{3}+5^{3}+6^{3}}}$$

Calculate 4 to the power of 3 and get 64.

$$\sqrt{\frac{1225}{36+64+5^{3}+6^{3}}}$$

Add 36 and 64 to get 100.

$$\sqrt{\frac{1225}{100+5^{3}+6^{3}}}$$

Calculate 5 to the power of 3 and get 125.

$$\sqrt{\frac{1225}{100+125+6^{3}}}$$

Add 100 and 125 to get 225.

$$\sqrt{\frac{1225}{225+6^{3}}}$$

Calculate 6 to the power of 3 and get 216.

$$\sqrt{\frac{1225}{225+216}}$$

Add 225 and 216 to get 441.

$$\sqrt{\frac{1225}{441}}$$

Reduce the fraction \frac{1225}{441} to lowest terms by extracting and canceling out 49.

$$\sqrt{\frac{25}{9}}$$

Rewrite the square root of the division \frac{25}{9} as the division of square roots \frac{\sqrt{25}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{5}{3}$$

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$