Use prime factorization to simplify the following square root leave as exact answer. How do you find the prime factors of this problem?

112 square root

112 = 16 x 7

so √112 = √16 √7
= 4√7

thank you

To find the prime factors of a number, you need to break it down into its prime factors, which are the prime numbers that divide the number exactly without leaving a remainder.

Let's find the prime factors of 112:

First, start by dividing the number by the smallest prime number, which is 2. If the number is divisible by 2, continue dividing it by 2 until it is no longer divisible.

112 ÷ 2 = 56
56 ÷ 2 = 28
28 ÷ 2 = 14
14 ÷ 2 = 7

Now, 7 is a prime number, so we cannot divide it further. Therefore, the prime factors of 112 are 2, 2, 2, and 7.

To simplify the square root of 112, we can express it as the product of its prime factors raised to half of their exponent.

√112 = √(2^3 x 7)

Since the square root of each factor will be taken individually, we can simplify this expression further:

√112 = √(2^3) x √7

Now, simplify each factor individually:

√(2^3) = 2^(3/2) = 2√2
√7 = √7

So, the simplified square root of 112 is:

√112 = 2√2√7

Please note that √2√7 is the exact answer, and it is not possible to simplify it further.