To express [tex]\(\frac{\sqrt{972}}{\sqrt{4}}\)[/tex] in its simplest radical form, we need to follow these steps:
1. Simplify the square roots individually:
- The square root of 4 is straightforward.
[tex]\[
\sqrt{4} = 2
\][/tex]
- The square root of 972 requires breaking down into its prime factors or identifying perfect squares.
[tex]\[
\sqrt{972} \approx 31.176914536239792
\][/tex]
2. Set up the division of the simplified square roots:
- Now that we have the simplified forms of each square root, we can proceed with the division.
[tex]\[
\frac{\sqrt{972}}{\sqrt{4}} = \frac{31.176914536239792}{2}
\][/tex]
3. Perform the division:
- Dividing the square root of 972 by the square root of 4,
[tex]\[
\frac{31.176914536239792}{2} = 15.588457268119896
\][/tex]
Therefore, the expression [tex]\(\frac{\sqrt{972}}{\sqrt{4}}\)[/tex] simplifies to [tex]\(15.588457268119896\)[/tex]. This is the simplest form for the given radical expression.
