What is \sqrt[3]{50^2} ?

The solution to \sqrt[3]{50^2} is 5\sqrt[3]{20}

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simplify \sqrt[3]{50^2}

simplify

3 5 0^{2}

5320

Decimal

13.57208 \dots

Solution steps

3 5 0^{2}

5 0^{2} = 2500

= 32500

Prime factorization of

2500 : 2^{2} \cdot 5^{4}

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

Apply exponent rule:

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

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

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

Apply radical rule:

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

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

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

Apply radical rule:

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

3 5^{3} = 5

= 5 3 2^{2} \cdot 5

2^{2} = 4

= 5 3 4 \cdot 5

Multiply the numbers:

4 \cdot 5 = 20

= 5320

7.5 \cdot 1 0^{- 4}

22 (2)

(1 + x^{3})^{- \frac{1}{2}}

4 e^{- 3 t}

- e^{- x} \cdot e^{3 x}