What is the irrational square root 28−−√ simplified?(1 point) Responses 214−−√ 2 start root 14 end root 47–√ 4 start root 7 end root 4–√ ⋅ 7–√ start root 4 end root times start root 7 end root 27–√
The simplified form of the irrational square root of 28 is 2√7.
To simplify the expression √28, we can break it down into factors:
First, find the perfect square factors of 28:
28 = 4 × 7
Next, split the square root:
√(4 × 7)
Since 4 is a perfect square, we can take its square root as a whole number:
= 2
The square root of 7 cannot be simplified further, so we leave it under the radical:
= 2√7
Therefore, the simplified form of √28 is 2√7.
To simplify the irrational square root √28, we can start by finding the prime factorization of 28.
The prime factorization of 28 is 2 × 2 × 7.
Now, we group the factors into pairs and bring out one factor from each pair to bring out perfect squares. In this case, we have one pair of 2s and one 7.
√28 = √(2 × 2 × 7)
Taking out the perfect square, we have:
√(2 × 2 × 7) = 2 × √7
Therefore, the simplified form of √28 is 2√7.
So, the correct answer is 2√7.