Solve sqrt[3]{999(999^2+3*999+3)+1}

$$\sqrt[ 3 ] { 999 ( 999 ^ { 2 } + 3 \times 999 + 3 ) + 1 }$$

Evaluate

$$1000$$

Solution Steps

Calculate 999 to the power of 2 and get 998001.

$$\sqrt[3]{999\left(998001+3\times 999+3\right)+1}$$

Multiply 3 and 999 to get 2997.

$$\sqrt[3]{999\left(998001+2997+3\right)+1}$$

Add 998001 and 2997 to get 1000998.

$$\sqrt[3]{999\left(1000998+3\right)+1}$$

Add 1000998 and 3 to get 1001001.

$$\sqrt[3]{999\times 1001001+1}$$

Multiply 999 and 1001001 to get 999999999.

$$\sqrt[3]{999999999+1}$$

Add 999999999 and 1 to get 1000000000.

$$\sqrt[3]{1000000000}$$

Calculate \sqrt[3]{1000000000} and get 1000.

$$1000$$

Factor

$$2^{3}\times 5^{3}$$