Simplify: (∛125 + ∛64 - ∛1)^1/3
2 answers:
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
<u>Answer</u><u>:</u> Hence, the simplified form of , {∛(125) + ∛(64) - ∛(1)}^(1/3) is 2.
<u>also</u><u> read</u><u> similar</u><u> questions</u><u>:</u> Simplify: ∛(2) × 2^(-1/13) × ¹²√(32) simplify : \sqrt[3]{2} \times {2}^{ - \frac{1}{13} } \times \sqrt[12]{32} \\ [...
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Answer:
20 ft long; 12 ft wide
Step-by-step explanation:
Let w = the width of the garden
Then l = w + 8
A = lw
A = (w + 8)w
=====
The sidewalk is 4 ft wide, so, for the big rectangle consisting of garden plus sidewalk:
Width = w +8
Length = w + 16
Area = (w + 8)(w + 16)
=====
The <em>difference</em> between the two areas is the area of the sidewalk (320 ft²).
(w + 8)(w + 16) - (w + 8)w = 320 Factor out w + 8
(w+ 8)(w + 16 – w) = 320 Combine like terms
(w+ 8) × 16 = 320 Divide each side by 16
w + 8 = 20 Subtract 8 from each side
w = 12 ft
l = 12 + 8
l = 20 ft
The garden is 20 ft long by 12 ft wide.
