Which is the reciprocal of √13?
Answer and explanation
Correct answer: 1/√13
The governing concept is the reciprocal of a non-zero number. For any non-zero number x, its reciprocal is 1/x, because multiplying the two gives x × (1/x) = 1. Since √13 is positive and therefore non-zero, its reciprocal is 1/√13, so option B is correct. The answer can also be written in rationalised form as √13/13: multiply numerator and denominator of 1/√13 by √13 to obtain √13/(√13)² = √13/13. Both forms have exactly the same value. Option D is the original number, option C is its square, and option A is its negative. In fact, √13 × (−√13) = −13, not 1, so option A cannot be a reciprocal.
Frequently asked questions
What is the correct answer to this question?
1/√13
Why is this the correct answer?
The governing concept is the reciprocal of a non-zero number. For any non-zero number x, its reciprocal is 1/x, because multiplying the two gives x × (1/x) = 1. Since √13 is positive and therefore non-zero, its reciprocal is 1/√13, so option B is correct. The answer can also be written in rationalised form as √13/13: multiply numerator and denominator of 1/√13 by √13 to obtain √13/(√13)² = √13/13. Both forms have exactly the same value. Option D is the original number, option C is its square, and option A is its negative. In fact, √13 × (−√13) = −13, not 1, so option A cannot be a reciprocal.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Irrational numbers.
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