What is the irrational square root 28−−√ simplified?(1 point)
Responses
4–√ ⋅ 7–√
start root 4 end root times start root 7 end root
27–√
2 start root 7 end root
47–√
4 start root 7 end root
214−−√
5 start root 7 end root
To simplify the irrational square root of 28, we can factor out perfect squares from under the square root sign:
28 = 4 × 7
So, we can rewrite the square root of 28 as the square root of 4 × 7.
Taking the square root of each perfect square separately:
√4 = 2
√7 remains as it is.
Therefore, the simplified form of the square root of 28 is:
2√7
OUT OF THE RESPONSES
Apologies for the confusion. The correct simplified form of the square root of 28 is indeed 2√7.
To simplify the expression √28, we need to find the largest perfect square that is a factor of 28. The largest perfect square that divides 28 is 4 (2^2).
Step 1: Split 28 into its factors:
28 = 4 * 7
Step 2: Simplify the square root expression:
√28 = √(4 * 7)
Step 3: Use the property that √(ab) = √a * √b:
√(4 * 7) = √4 * √7
Step 4: Simplify the square root of 4:
√4 = 2
Step 5: Combine the simplified square roots:
√28 = 2 * √7
Therefore, the simplified form of √28 is 2√7.