To simplify \(\sqrt{2520}\), we'll break it down into its prime factors:

### Step 1: Find the prime factorization of 2520.

Start by dividing 2520 by the smallest prime number (2) until it’s no longer divisible by 2.

\[
2520 \div 2 = 1260
\]
\[
1260 \div 2 = 630
\]
\[
630 \div 2 = 315 \quad (\text{315 is odd, so stop dividing by 2})
\]

Now divide by 3 (next smallest prime):

\[
315 \div 3 = 105
\]
\[
105 \div 3 = 35
\]

Next, divide by 5:

\[
35 \div 5 = 7
\]

Finally, 7 is prime.

So, the prime factorization of 2520 is:
\[
2520 = 2^3 \times 3^2 \times 5 \times 7
\]

### Step 2: Simplify the square root.

\[
\sqrt{2520} = \sqrt{2^3 \times 3^2 \times 5 \times 7}
\]

We can pair the prime factors where possible:

\[
\sqrt{2520} = \sqrt{(2^2) \times 2 \times (3^2) \times 5 \times 7}
\]

Now, take the square root of the perfect squares:

\[
\sqrt{2520} = 2 \times 3 \times \sqrt{2 \times 5 \times 7}
\]

\[
\sqrt{2520} = 6 \times \sqrt{70}
\]

So, the simplified form of \(\sqrt{2520}\) is:

\[
6\sqrt{70}
\]

Would you like any further explanations or help with a different concept? Here are some related questions you might find interesting:

1. How do you simplify square roots of numbers that aren't perfect squares?
2. How can prime factorization help in simplifying other square roots?
3. Can you simplify \(\sqrt{980}\) in a similar way?
4. What is the fastest method for finding the prime factorization of a large number?
5. How does square root simplification apply to real-world scenarios?

**Tip**: Always look for perfect square factors first when simplifying square roots! It helps reduce the complexity of the problem.

Learn how to simplify √2520 step by step using prime factorization. This method helps break down the square root into its simplest form: 6√70. Suitable for students in Grades 8-10, covering key mathematical concepts such as square roots and factorization.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation