Question

Isn’t it just 5? Why would it say check all that apply

Answer 1

A. 5

B.
`25^{(1)/(2) }`

D. -5

E.
`-25^{(1)/(2) }`

Explanation:

A number has a square root when a certain number can be multiplied by twice by itself to get the same number for the answer.

When you multiply 5 by 5, you get 25.

When you multiply
`25^{(1)/(2) }` by
`25^{(1)/(2) }`, you get 25. This is because
`25^{(1)/(2) }` can also be written as
`√(25)`, which gives you 5, and when you multiply them together it produced a product of 25.

When you multiply -5 by -5, you also get 25 (this is because when a negative number is multiplied by another negative, the product is a positive).

When you multiply
`-25^{(1)/(2) }` by
`-25^{(1)/(2) }`, you also get 25. Similar as with answer "B," you will get the answer of -5, and multiplying these by itself will give you 25.

All the other numbers cannot be multiplied by itself to get the answer of 25.

Answer 2

Answer:
`25^(1)/(2)`

Explanation:

25 = 5*5 or -5 * -5

yes, that is correct. However, you forgot another property of roots. Roots are simply exponential fractions.

`\sqrt[n]{x^m}=x^(m)/(n)`

Therefore,
`√(25)` can also be rewritten as:
`25^(1)/(2)`. Notice that it cannot be -25 because that would be a negative square root which will give us an imaginary number.