How to solve roots 56 raised to the power 1/2

To solve the expression (56)^(1/2), we need to find the square root of 56. Here's a step-by-step explanation of how to do it:

Step 1: Prime Factorization
Start by finding the prime factors of 56. Prime factorization is the process of breaking down a number into its prime factors. Let's calculate the prime factorization of 56:

56 = 2 * 2 * 2 * 7

Step 2: Pairing Factors
Now, pair the factors in twos:

(2 * 2) * (2 * 7)

Step 3: Simplify the Pairs
Simplify each pair by multiplying the factors together:

4 * 14

Step 4: Multiply the Simplified Pairs
Multiply the simplified pairs together:

4 * 14 = 56

Step 5: Square Root
The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we need to find the square root of 56:

√56 = √(4 * 14)

Step 6: Simplify the Square Root
Simplify the square root expression by separating the square numbers from the non-square numbers:

√(4 * 14) = √4 * √14

Step 7: Calculate the Square Root
Calculate the square root of the square numbers and leave the non-square numbers under the square root sign:

√4 * √14 = 2 * √14

Step 8: Final Answer
Therefore, the square root of 56 is 2√14.

Summary:
To solve the expression (56)^(1/2), we first found the prime factorization of 56, which is 2 * 2 * 2 * 7. Then, we paired the factors and simplified them to 4 * 14. Next, we took the square root of 4, which is 2, and left the square root of 14 under the square root sign. Thus, the final answer is 2√14.