The real cube root of negative 64 is –4, since (–4) × (–4) × (–4) = –64.
What is the real cube root of 64?
The real cube root of 64 is 4, because 4 × 4 × 4 = 64.
In other words, ∛64 = 4. Ever stacked 64 identical cubes into a larger 4 × 4 × 4 shape? You’ve basically built the geometric version of this cube root.
Can a real cube root be negative?
Yes, a real cube root can be negative when the original number is negative.
Odd roots (cube, fifth, seventh, etc.) treat negative numbers like negative positives, so the root keeps the same sign. Think of it this way: stacking layers of –2 gives –8, not 8.
What is the cube root of a negative real number?
The cube root of any negative real number is negative.
That’s the key difference between cube roots and square roots. The cube root of –x equals –∛x, so the sign flips right along with the magnitude.
Is negative 64 a perfect cube?
Yes, negative 64 is a perfect cube because it equals (–4)³.
A perfect cube is just any integer that can be written as n³ for some integer n, and –4 is definitely an integer.
Which statement is true if A is the third root of 64?
A = 4 (and the third root of –64 is –4).
If A³ = 64, then A must be 4; if A³ = –64, A must be –4. No other integer cubed lands on 64 or –64.
What is the cube root of 1000?
The cube root of 1000 is 10.
Check it: 10 × 10 × 10 = 1000. That’s why a cube 10 units on each side has a volume of exactly 1000 cubic units.
Is cube root Plus or minus?
Cube root isn’t restricted to “plus-or-minus” like square roots are; it gives a single real answer for every real input.
In the complex plane there are three cube roots of 1, but in real numbers there’s only one—and it’s positive for positive inputs and negative for negative inputs.
How do you find the cube root of 9261?
One fast way is to recall that 21³ = 9261, so ∛9261 = 21.
Start with cubes you know (10³ = 1,000; 20³ = 8,000) and work your way up. A calculator or spreadsheet can also compute it directly.
What is the cube of negative 1?
The cube of –1 is –1, because (–1) × (–1) × (–1) = –1.
It’s the only integer that cubes to itself, which is why –1 pops up in countless physics and engineering formulas.
What are the cube roots of 1?
The real cube root of 1 is 1; the other two roots are complex.
In real numbers, x³ = 1 has exactly one solution: x = 1. The complex solutions are –½ ± i√3⁄2.
What is a cube root of 729?
One cube root of 729 is 9, because 9 × 9 × 9 = 729.
If you factor 729, you’ll see 9³ = (3²)³ = 3⁶, making 729 a perfect cube.
Can perfect cubes be negative?
Yes, perfect cubes can be negative; for example, –125 is a perfect cube because (–5)³ = –125.
Any integer cubed gives either a positive or negative perfect cube, depending on the sign of the base.
Is 8 a perfect cube?
Yes, 8 is a perfect cube because 2³ = 8.
That’s why a 2 × 2 × 2 arrangement of unit cubes has a total volume of 8.
Is 64 a perfect square?
Yes, 64 is a perfect square because 8² = 64.
It’s also a perfect cube (4³ = 64), making it a rare “perfect sixth power.” Honestly, this is one of those numbers that feels like it’s showing off.
