What type of number is 3√5?
Answer and explanation
Correct answer: Irrational number
The number √5 is irrational because 5 is not a perfect square. Multiplying an irrational number by a non-zero rational number remains irrational. Here 3 is a non-zero rational number. For a short proof, suppose 3√5 were rational; dividing it by 3, a non-zero rational, would imply √5 is rational, which is impossible. Hence 3√5 is irrational, so option A is correct. It is not rational or an integer, and it is not zero because both 3 and √5 are positive. The common error is to think that multiplying by an integer automatically removes irrationality; that happens only in special expressions involving cancellation, not when a non-zero rational multiplies √5. The classification depends on the irrational factor and the non-zero multiplier.
Frequently asked questions
What is the correct answer to this question?
Irrational number
Why is this the correct answer?
The number √5 is irrational because 5 is not a perfect square. Multiplying an irrational number by a non-zero rational number remains irrational. Here 3 is a non-zero rational number. For a short proof, suppose 3√5 were rational; dividing it by 3, a non-zero rational, would imply √5 is rational, which is impossible. Hence 3√5 is irrational, so option A is correct. It is not rational or an integer, and it is not zero because both 3 and √5 are positive. The common error is to think that multiplying by an integer automatically removes irrationality; that happens only in special expressions involving cancellation, not when a non-zero rational multiplies √5. The classification depends on the irrational factor and the non-zero multiplier.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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