What is Cube Root of 1000

• Cube root of 1000 is written as $\sqrt[3]{1000}$ (Radical form).
• $\sqrt[3]{1000}$ = $\sqrt[3]{10 \times 10 \times 10}$ = 10
• In the exponential form, the cube root of 1000 is expressed as $(1000)^\frac{1}{3}$.

Prime Factorization Method

• Step 1: Prime factors of 1000: 2 x 2 x 2 x 5 x 5 x 5
• Step 2: Prime factors of 1000 in triplets: (2 x 2 x 2) x (5 x 5 x 5)
• Step 3: Now cube root of 1000:

$\sqrt[3]{1000} = \sqrt[3]{(2 \times 2 \times 2) \times (5 \times 5 \times 5)}$

$\sqrt[3]{1000} = \sqrt[3]{ 2^3 \times5^3}$

$\sqrt[3]{1000} = \sqrt{(2\times5)^3}$

$\sqrt[3]{1000} = \sqrt{10^3}$

$\sqrt[3]{1000} = 10$

Therefore, the cube root of 1000 is 10