Question

Simplify: (∛125 + ∛64 - ∛1)^1/3​

Answer 1

Answer:

2

Step-by-step explanation:

(∛125 + ∛64 - ∛1)^1/3​

(5 + 4 - 1)^1/3

8^1/3

= 2

Answer 2

Step-by-step explanation:

Given that: {∛(125) + ∛(64) - ∛(1)}^(1/3)

= {∛(5 * 5 * 5) + ∛(4 * 4* 4) -∛(1)}^(1/3)

= {∛(5³) + ∛(4³) - ∛(1)}^(1/3)

[since, ⁿ√(a) = a^(1/n)]

= {(5³)^(1/3) + (4³)^(1/3) - (1)^(1/3)}^(1/3)

[since, (aᵐ)ⁿ = aᵐⁿ}

= {(5)^{3*(1/3)} + (4)^{3*(1/3)} - (1*1*1)}^(1/3)

= {{5)^1 + (4)^1 - 1}^(1/3)

= (5 + 4 -1)^(1/3)

= (9 - 1)^(1/3)

= 8^(1/3)

= (2*2*2)^(1/3)

= (2³)^(1/3)

[since, (aᵐ)ⁿ = aᵐⁿ]

= (2)^{3*(1/3)}

= (2)¹

= 2

Therefore, {∛(125) + ∛(64) - ∛(1)}^(1/3) = 2

Answer: Hence, the simplified form of , {∛(125) + ∛(64) - ∛(1)}^(1/3) is 2.

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