To simplify the expression \( \sqrt{2512} \), let's break down the number into its prime factors.
First, we can factor \( 2512 \):
- \( 2512 \div 2 = 1256 \)
- \( 1256 \div 2 = 628 \)
- \( 628 \div 2 = 314 \)
- \( 314 \div 2 = 157 \)
Since \( 157 \) is a prime number, we have: \[ 2512 = 2^4 \times 157 \]
Now, we can apply the square root: \[ \sqrt{2512} = \sqrt{2^4 \times 157} = \sqrt{2^4} \times \sqrt{157} = 4\sqrt{157} \]
So, the simplest form of \( \sqrt{2512} \) is \( 4\sqrt{157} \).
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