Which is the simplest form of \(\sqrt{245}\) for understanding its position on the number line?
Answer and explanation
Correct answer: \(7\sqrt{5}\)
Since \(245=49\times5\) and 49 is the largest perfect-square factor, \(\sqrt{245}=\sqrt{49\times5}=7\sqrt{5}\). Option A would represent \(\sqrt{175}\), not \(\sqrt{245}\), and \(\sqrt{49}+\sqrt{5}\) is not equal to \(\sqrt{49+5}\). Exam tip: factor the number using its largest perfect-square factor before simplifying a square root.
Frequently asked questions
What is the correct answer to this question?
\(7\sqrt{5}\)
Why is this the correct answer?
Since \(245=49\times5\) and 49 is the largest perfect-square factor, \(\sqrt{245}=\sqrt{49\times5}=7\sqrt{5}\). Option A would represent \(\sqrt{175}\), not \(\sqrt{245}\), and \(\sqrt{49}+\sqrt{5}\) is not equal to \(\sqrt{49+5}\). Exam tip: factor the number using its largest perfect-square factor before simplifying a square root.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Representing real numbers on the number line.
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