What is \sqrt[3]{200^2} ?

The solution to \sqrt[3]{200^2} is 20\sqrt[3]{5}

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simplify \sqrt[3]{200^2}

simplify

3 20 0^{2}

2035

Decimal

34.19951 \dots

Solution steps

3 20 0^{2}

20 0^{2} = 40000

= 340000

Prime factorization of

40000 : 2^{6} \cdot 5^{4}

= 3 2^{6} \cdot 5^{4}

Apply exponent rule:

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

2^{6} \cdot 5^{4} = 2^{6} \cdot 5^{3} \cdot 5

= 3 2^{6} \cdot 5^{3} \cdot 5

3 2^{6} \cdot 5^{3} \cdot 5 = 3 2^{6} 3 5^{3} 35

= 3 2^{6} 3 5^{3} 35

3 2^{6} = 4

= 4 3 5^{3} 35

Apply radical rule:

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

3 5^{3} = 5

= 4 \cdot 535

Multiply the numbers:

4 \cdot 5 = 20

= 2035

(3 x^{2}) (5 x^{2})

0.5 \cdot 1 0^{- 8}

- 4 e^{- 1}

0.5 \cdot 1 0^{- 9}

(x^{2} - 4)^{4}