What is the irrational square root √28 simplified?(1 point)
Responses
4√7
4 start root 7 end root
√4 ⋅ √7
start root 4 end root times start root 7 end root
2√7
2 start root 7 end root
2√14
2√7
To simplify the square root of 28, we can factor it into its prime factors. The prime factorization of 28 is 2 * 2 * 7.
Taking the square root of 2 * 2 * 7, we can simplify it as follows:
√(2 * 2 * 7) = √(2 * 2) * √7 = 2 * √7 = 2√7
Therefore, the simplified form of the square root of 28 is 2√7.
To simplify the irrational square root √28, we need to find the largest perfect square factor of 28.
First, we can break down 28 into its prime factors: 2 * 2 * 7.
Since 2 * 2 = 4, which is a perfect square, we can simplify the square root of 28 as follows:
√28 = √(4 * 7)
Using the property of square roots that says √(a * b) = √a * √b, we can separate the perfect square factor:
√(4 * 7) = √4 * √7
√4 is equal to 2, so the simplified form of √28 is:
2√7