Which of the following is the simplified form of \(\sqrt{28}\)?
Answer and explanation
Correct answer: \(2\sqrt{7}\)
\(\sqrt{28}=\sqrt{4\times7}=\sqrt{4}\cdot\sqrt{7}=2\sqrt{7}\). The perfect square 4 is taken outside the radical, giving the principal (positive) square root. Option D is incorrect because the principal square root is non-negative, so \(-2\sqrt{7}\) is not the simplified value. Option C (\(\sqrt{14}\)) comes from a mistaken grouping and does not equal \(2\sqrt{7}\). Option B (\(4\sqrt{7}\)) would imply \(28=16\times7\), which is false. Exam tip: factor out the largest perfect-square factor to simplify radicals efficiently.
Frequently asked questions
What is the correct answer to this question?
\(2\sqrt{7}\)
Why is this the correct answer?
\(\sqrt{28}=\sqrt{4\times7}=\sqrt{4}\cdot\sqrt{7}=2\sqrt{7}\). The perfect square 4 is taken outside the radical, giving the principal (positive) square root. Option D is incorrect because the principal square root is non-negative, so \(-2\sqrt{7}\) is not the simplified value. Option C (\(\sqrt{14}\)) comes from a mistaken grouping and does not equal \(2\sqrt{7}\). Option B (\(4\sqrt{7}\)) would imply \(28=16\times7\), which is false. Exam tip: factor out the largest perfect-square factor to simplify radicals efficiently.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
