Find the square root of the following by prime factorization 7056

7056 = 2 * 3528 = 2^2 * 1714 = 2^3 * 857

Now factor 857. You know there are no more 2's in there, so start with 3, and so on.

So, what do you get? Since there are only three 2's, the square root will not be an integer, but will have a radical left over.

7056 = (2*2*2*2)*(3*3)*(7*7)

= 16*9*49

so √7056 = 4*3*7 = 84

I see I can neither factor nor count. Go with Reiny.

To find the square root of 7056 by prime factorization, you need to follow these steps:

Step 1: Prime Factorization
The first step is to find the prime factorization of 7056. We divide the number by its smallest prime factor, which is 2.

7056 ÷ 2 = 3528

Now, we divide the quotient (3528) by 2 again:

3528 ÷ 2 = 1764

Continuing this process, we get:

1764 ÷ 2 = 882
882 ÷ 2 = 441
441 ÷ 3 = 147
147 ÷ 3 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1

So, the prime factorization of 7056 is 2 × 2 × 2 × 2 × 3 × 3 × 7 × 7.

Step 2: Grouping the Factors
Group the prime factors of 7056 in pairs:

(2 × 2) × (2 × 2) × (3 × 3) × (7 × 7)

Step 3: Take Out One Factor from Each Pair
Take out one factor from each pair and write it outside the square root sign:

2 × 2 × 3 × 7

Step 4: Simplify
Multiply the factors outside the square root sign:

2 × 2 × 3 × 7 = 84

So, the square root of 7056 is √7056 = 84.