What is √54 simplified?
The square root of 54 simplified is approximately 7.348
To simplify √54, we can factorize the number inside the square root.
First, we find the prime factorization of 54:
54 = 2 * 3 * 3 * 3
Next, we group the prime factors:
54 = 2 * (3 * 3 * 3)
Now, we can take out pairs of the same prime factors:
54 = 2 * (3^2 * 3)
Simplifying further:
54 = 2 * 3^3
Taking the square root:
√54 = √(2 * 3^3)
Finally, we can break it down:
√54 = √2 * √(3^3)
So, the simplified form is:
√54 = 3√2
To simplify the square root of 54 (√54), we need to find the factors of 54 and try to simplify the square root expression by factoring out any perfect square factors.
Step 1: Find the factors of 54:
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.
Step 2: Identify any perfect square factors:
Among the factors of 54, 9 is a perfect square because it can be expressed as 3^2.
Step 3: Simplify the square root expression by factoring out the perfect square:
Now, let's rewrite √54 as √(9 × 6).
Step 4: Simplify the expression:
Using the property of square roots that states √(a × b) = √a × √b, we can break down the square root expression further: √(9 × 6) = √9 × √6.
Step 5: Evaluate the simplified expression:
√9 = 3 (since 9 is a perfect square).
Therefore, √54 = 3√6.
So, the simplified form of √54 is 3√6.