What is \sqrt[3]{20000} ?

The solution to \sqrt[3]{20000} is 10\sqrt[3]{20}

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simplify \sqrt[3]{20000}

simplify

320000

10320

Decimal

27.14417 \dots

Solution steps

320000

Prime factorization of

20000 : 2^{5} \cdot 5^{4}

= 3 2^{5} \cdot 5^{4}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

2^{5} \cdot 5^{4} = 2^{3} \cdot 2^{2} \cdot 5^{3} \cdot 5

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

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

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

Apply radical rule:

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

3 2^{3} = 2

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

Apply radical rule:

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

3 5^{3} = 5

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

Multiply the numbers:

2 \cdot 5 = 10

= 10 3 2^{2} \cdot 5

2^{2} = 4

= 10 3 4 \cdot 5

Multiply the numbers:

4 \cdot 5 = 20

= 10320

lo g_{5} (5^{x})

\frac{81}{24}

(2 x - 3) (x + 4)

\frac{81}{12}

354 + 224