What is \sqrt[3]{1500} ?

The solution to \sqrt[3]{1500} is 5\sqrt[3]{12}

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simplify \sqrt[3]{1500}

simplify

31500

5312

Decimal

11.44714 \dots

Solution steps

31500

Prime factorization of

1500 : 2^{2} \cdot 3 \cdot 5^{3}

= 3 2^{2} \cdot 3 \cdot 5^{3}

Apply radical rule:

n ab = n a n b, a \geq 0, b \geq 0

3 2^{2} \cdot 3 \cdot 5^{3} = 3 2^{2} \cdot 3 3 5^{3}

= 3 2^{2} \cdot 3 3 5^{3}

Apply radical rule:

n a^{n} = a, a \geq 0

3 5^{3} = 5

= 3 2^{2} \cdot 3 \cdot 5

2^{2} = 4

= 3 4 \cdot 3 \cdot 5

Multiply the numbers:

4 \cdot 3 = 12

= 312 \cdot 5

= 5312

n (n - 1)

(- 3)^{8}

\frac{1 2 ^{3} \cdot 6 ^{5}}{9 ^{4} \cdot 2 ^{10}}

(7 - 6 i) (3 + 2 i)

7 (- 2 y + 8)