A base player throws the ball from home plate to second base, a distance measured to be square root of 7200 feet. What simplified radical is equivalent to this value?

To simplify the radical \(\sqrt{7200}\), we start by finding the prime factorization of 7200.

First, let's break down 7200 into its prime factors:

\[
7200 \div 2 = 3600
\]
\[
3600 \div 2 = 1800
\]
\[
1800 \div 2 = 900
\]
\[
900 \div 2 = 450
\]
\[
450 \div 2 = 225
\]
\[
225 \div 3 = 75
\]
\[
75 \div 3 = 25
\]
\[
25 \div 5 = 5
\]
\[
5 \div 5 = 1
\]

So, the prime factorization of 7200 is:

\[
7200 = 2^4 \times 3^2 \times 5^2
\]

Now, let's simplify the square root:

\[
\sqrt{7200} = \sqrt{2^4 \times 3^2 \times 5^2}
\]

Each square root of a square can be taken out of the radical:

\[
\sqrt{7200} = \sqrt{(2^2 \times 3 \times 5) \times (2^2 \times 3 \times 5)}
\]

\[
\sqrt{7200} = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60
\]

Thus, the simplified radical form of \(\sqrt{7200}\) is \(60\sqrt{2}\).

If you have any more questions or want further details, feel free to ask!

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Here are 8 related questions to consider:

1. What is the value of \(\sqrt{1800}\) in simplified radical form?
2. How do you simplify the square root of a product of primes?
3. What is the length of the hypotenuse in a right triangle with legs of 6 and 8 units?
4. How can you simplify \(\sqrt{1250}\)?
5. What is the simplified radical form of \(\sqrt{200}\)?
6. How do you calculate the distance between two points on a coordinate plane?
7. What is the square root of 50 in simplified form?
8. What is the square root of 288 in simplified radical form?

**Tip:** When simplifying radicals, always factor the number into primes first to identify perfect squares that can be simplified outside the radical.

Learn how to simplify the square root of 7200 step-by-step with a detailed solution. This problem involves radicals and prime factorization, essential for high school math students.

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