How do you find the square root of 54?

To find the square root of 54, follow these steps:

Understand the Problem: The goal is to determine the value of √54, which is a number that, when multiplied by itself, gives 54.

Check for Simplification:

Factorize 54 into its prime factors: 54 = 2 × 3 × 3 × 3 (or 54 = 2 × 3² × 3).
Pair the factors: From the factorization, we can simplify √54 as follows: √54 = √(2 × 3² × 3) = √(3²) × √(2 × 3). The square root of 3² is 3, so: √54 = 3 × √6.
Thus, the simplified form of √54 is 3√6.

Approximate the Value: To find an approximate decimal value:

√6 ≈ 2.449 (using a calculator or estimation methods).
Multiply this by 3: 3 × 2.449 = 7.347.
Final Answer: The exact form of the square root of 54 is 3√6.
The approximate decimal value of the square root of 54 is 7.35 (rounded to two decimal places).