What is the irrational square root √28 simplified?
1. 2√14
2. √4 · √7
3. 2√7
4. 4√7
The simplified irrational square root of √28 is 2√7. Therefore, the correct answer is option 3.
To simplify the irrational square root √28, we need to find the largest perfect square that can be factored out from 28.
28 can be factored as 4 * 7.
Therefore, the simplified form of √28 is √(4 * 7).
This can be further simplified using the property √(ab) = √a * √b.
So, √(4 * 7) = √4 * √7.
The square root of 4 is 2, so the simplified form is 2√7.
Therefore, the correct answer is option 3. 2√7.
To simplify the irrational square root √28, we need to express it as the product of a rational number and the square root of a smaller number.
One way to simplify square roots is to factorize the number inside the square root, if possible. In this case, we can factorize 28 as 2 * 2 * 7.
Now, we can rewrite the square root of 28 as √(2 * 2 * 7).
Next, we can separate the numbers inside the square root into two separate square roots:
√2 * √2 * √7
At this point, we can simplify the square root of 2 as √2 and the square root of 2 as √2.
So, the simplified form of √28 is √2 * √2 * √7, which is equivalent to 2√7.
Therefore, the correct answer is option 3: 2√7.