Question

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

Answer 1

Answer:

A. 5

B. $25^{\frac{1}{2} }$

D. -5

E. $-25^{\frac{1}{2} }$

Step-by-step 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 $25^{\frac{1}{2} }$ by $25^{\frac{1}{2} }$, you get 25. This is because $25^{\frac{1}{2} }$ can also be written as $\sqrt{25}$, 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 $-25^{\frac{1}{2} }$ by $-25^{\frac{1}{2} }$, 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: $25^\frac{1}{2}$

Step-by-step explanation:

25 = 5*5 or -5 * -5

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

$\sqrt[n]{x^m}=x^\frac{m}{n}$

Therefore, $\sqrt{25}$ can also be rewritten as: $25^\frac{1}{2}$. Notice that it cannot be -25 because that would be a negative square root which will give us an imaginary number.