What is the square root of 12 simplified
The square root of 12 simplified is 2√3.
What is the square root of 18 simplified?
What is the square root of 125 simplified?
The square root of 18 simplified is 3√2.
The square root of 125 simplified is 5√5.
To simplify the square root of 12, we need to break it down into its prime factors.
Step 1: Divide 12 by the smallest prime number, which is 2. We get 12 ÷ 2 = 6.
Step 2: Divide the result, 6, by another prime number, 2. We get 6 ÷ 2 = 3.
Step 3: Since 3 is a prime number, we cannot divide it further.
Therefore, the prime factorization of 12 is 2 × 2 × 3.
Next, we can simplify the square root expression:
√12 = √(2 × 2 × 3)
Using the property of square roots that says √(a × b) = √a × √b, we can separate the square root of each factor:
√12 = √2 × √2 × √3
Since the square root of 2 times itself is 2, we can simplify further:
√12 = 2√3
So, the simplified square root of 12 is 2√3.
To simplify the square root of 12, we need to find the largest perfect square that divides evenly into 12. In this case, the largest perfect square that divides evenly into 12 is 4 (since 4 * 3 = 12).
Now, we can rewrite the square root of 12 as the square root of 4 times the square root of 3.
√12 = √4 * √3.
The square root of 4 is 2, so we can simplify further:
√12 = 2√3.
Therefore, the square root of 12 simplified is 2√3.