Which of the following is an example where the sum of two irrational numbers is a rational number?
Answer and explanation
Correct answer: \(\sqrt{5}+(-\sqrt{5})\)
Both \(\sqrt{5}\) and \(-\sqrt{5}\) are irrational, but their sum \(\sqrt{5}+(-\sqrt{5})=0\) is rational, so A is correct. Closest distractor B, \(\sqrt{2}+\sqrt{7}\), remains irrational (sums of distinct square‑free roots are generally irrational). C gives \(\sqrt{3}+\sqrt{3}=2\sqrt{3}\), still irrational. D is a sum of a rational and an irrational, which is irrational. Exam tip: look for additive inverses — if both terms cancel each other, the sum is rational (often 0).
Frequently asked questions
What is the correct answer to this question?
\(\sqrt{5}+(-\sqrt{5})\)
Why is this the correct answer?
Both \(\sqrt{5}\) and \(-\sqrt{5}\) are irrational, but their sum \(\sqrt{5}+(-\sqrt{5})=0\) is rational, so A is correct. Closest distractor B, \(\sqrt{2}+\sqrt{7}\), remains irrational (sums of distinct square‑free roots are generally irrational). C gives \(\sqrt{3}+\sqrt{3}=2\sqrt{3}\), still irrational. D is a sum of a rational and an irrational, which is irrational. Exam tip: look for additive inverses — if both terms cancel each other, the sum is rational (often 0).
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.
