Respuesta :
The square root of a number is a value that, when multiplied by itself, gives the number. Example: 4 × 4 = 16, so a square root of 16 is 4. But note that (−4) × (−4) = 16 also, so −4 is also a square root of 16. This is why each nonzero interger has two square roots.
The cube root of a number is a special value that, when used in a multiplication three times, gives that number. Example: 3 × 3 × 3 = 27, so the cube root of 27 is 3. But cube root is unlike square root where as -3 × -3 × -3 = -27 not 27 therefore there is only one cube root.
I hope this helps
So we want to see why a cube root has only one real solution while a square root has two, let's analyze the operations.
First, you can remember the rule of signs:
(+)*(+) = (+)
(+)*(-) = (-)
(-)*(+) = (-)
(-)*(-) = (+)
Now, we can define the square root as the inverse of the square exponent.
so if:
A^2 = A*A
then
√(A^2) = A
Now, notice that when we work with square exponents, negative numbers multiply themselves, and because of the rule of the sign, the output is positive.
Notice that:
5*5 = 25 then √25 = 5
(-5)*(-5) = 25 then √25 = -5
So √25 has two possible solutions.
Now, a cube root is the inverse of an exponent 3.
so if:
A^3 = A*A*A
∛A^3 = A
Let's use the same values of before:
5*5*5 = 125 then √125 = 5
(-5)*(-5)*(-5) = 25*(-5) = (-125) then √-125 = -5
So using the same numbers as before, we got two different results, this is why the cube root one solution for each input.
And another thing that you can notice here, is that while the square root only takes inputs equal or larger than zero, the cube root works with negative inputs.
so for example with cubic roots we have:
∛(-125) = -5
∛125 = 5
while for square roots:
√25 = ±5
√(-25) = not a real number (a complex one)
If you want to read more about cube roots, you can read:
https://brainly.com/question/18510441
