Question

What is the simplest form of 2512
?(1 point)
Responses

25−−√
Start Root 25 End Root

25−−√12
root index Start Fraction 1 over 2 End Fraction Start Root 25 End Root

12.5
12.5

5
5

1 answer

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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