Question

When we simplify radicals containing integers, we are tasked first with identifying if theinteger inside the radical is perfect. What do you look for to determine if an integer ("just number") is perfect? Be specific and use a complete sentence.

Answer 1

In order to find if an integer is perfect, we need first to factor the number into prime factors.

For example, let's factor the number 16:

`16=2\cdot2\cdot2\cdot2=2^4`

Since the exponent of all prime factors is even, that means the number has a square root that is an integer:

`√(16)=√(2^4)=2^{(4)/(2)}=2^2=4`

Let's use another example: number 36:

`\begin{gathered} 36=2\cdot2\cdot3\cdot3=2^2\cdot3^2 \\ √(36)=√(2^2\cdot3^2)=2\cdot3=6 \end{gathered}`