Which option correctly describes the nature of (−√47)?
Answer and explanation
Correct answer: Irrational real number
The key criterion is that the square root of a positive integer is rational only when the integer is a perfect square. Since 47 is not a perfect square—it lies strictly between 36 = 6² and 49 = 7²—√47 is irrational. Negating a number changes its sign but does not change whether it is rational or irrational. Therefore −√47 is also irrational. It is still real because the square root of a positive real number is real, and the negative of a real number remains real. Hence option A is correct. It cannot be a rational number, whole number, or natural number, so options B, C, and D are excluded by the same reasoning.
Frequently asked questions
What is the correct answer to this question?
Irrational real number
Why is this the correct answer?
The key criterion is that the square root of a positive integer is rational only when the integer is a perfect square. Since 47 is not a perfect square—it lies strictly between 36 = 6² and 49 = 7²—√47 is irrational. Negating a number changes its sign but does not change whether it is rational or irrational. Therefore −√47 is also irrational. It is still real because the square root of a positive real number is real, and the negative of a real number remains real. Hence option A is correct. It cannot be a rational number, whole number, or natural number, so options B, C, and D are excluded by the same reasoning.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Irrational numbers.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
