Which statement is correct about (\sqrt{37})?
Answer and explanation
Correct answer: It is irrational
The square root of a whole number is rational only when the number under the root is a perfect square, such as \(1,4,9,16,25,36\), or another square of an integer. The number 37 lies between \(36=6^2\) and \(49=7^2\), so it is not a perfect square. Therefore \(\sqrt{37}\) cannot be written as an integer or as a terminating or repeating rational number; it is irrational.
Thus option A is correct. It is not a perfect square itself, because 37 is the radicand rather than a square number. Also, \(\sqrt{37}\) is slightly greater than 6, so it cannot equal 6; squaring 6 gives 36, not 37. It is not an integer for the same reason. The key test is that the square root of a positive integer is irrational when that integer is not a perfect square.
Frequently asked questions
What is the correct answer to this question?
It is irrational
Why is this the correct answer?
The square root of a whole number is rational only when the number under the root is a perfect square, such as \(1,4,9,16,25,36\), or another square of an integer. The number 37 lies between \(36=6^2\) and \(49=7^2\), so it is not a perfect square. Therefore \(\sqrt{37}\) cannot be written as an integer or as a terminating or repeating rational number; it is irrational.
Thus option A is correct. It is not a perfect square itself, because 37 is the radicand rather than a square number. Also, \(\sqrt{37}\) is slightly greater than 6, so it cannot equal 6; squaring 6 gives 36, not 37. It is not an integer for the same reason. The key test is that the square root of a positive integer is irrational when that integer is not a perfect square.
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.
