What is the irrational root 28 simplified?
√28 cannot be simplified further because it is already in its simplest radical form.
To find the simplified form of the irrational root of 28, we can first determine if 28 is a perfect square. If it is, then the square root is a rational number; otherwise, it is an irrational number.
In this case, 28 is not a perfect square because there is no whole number that, when squared, equals 28. Therefore, the square root of 28 is an irrational number.
To simplify the square root of 28, we can express it as the product of the square root of a perfect square and the square root of the remaining factor(s).
The prime factorization of 28 is 2 × 2 × 7. We can simplify the square root of 28 as √(2^2 × 7).
Taking the square root inside the radical separately, we have √(2^2) × √7.
The square root of 2^2 is 2, so we get 2√7.
Therefore, the simplified form of the irrational root of 28 is 2√7.
To find the simplified form of the irrational root of 28, we need to determine if it can be simplified further by factoring out any perfect squares from the radicand (the number under the square root symbol).
Step 1: Find the prime factorization of 28:
The prime factors of 28 are 2 * 2 * 7.
Step 2: Group the prime factors into pairs:
Since there are two 2's, we can pair them together. However, we don't have any pairs for the prime factor 7.
Step 3: Simplify the perfect squares outside the square root symbol:
The pair of 2's can be simplified as √(2 * 2) = 2. We then multiply the unsimplified factors, which in this case is 7, to get √(7).
Therefore, the simplified form of the irrational root of 28 is 2√(7).