What is the rationalized form of 1/(√5 − 2)?
Answer and explanation
Correct answer: √5 + 2
Rationalization removes a radical from a denominator by multiplying the numerator and denominator by the denominator’s conjugate. The conjugate of √5 − 2 is √5 + 2. Therefore, 1/(√5 − 2) = (√5 + 2)/[(√5 − 2)(√5 + 2)]. Applying the difference-of-squares identity gives the denominator 5 − 4 = 1, so the fraction simplifies to √5 + 2. Hence option A is correct. Option B is merely the original denominator expression and does not rationalize the fraction. Option C introduces an unsupported factor of 9, while option D is not equivalent to the original fraction. The essential step is choosing the conjugate, which converts the radical denominator into a rational number.
Frequently asked questions
What is the correct answer to this question?
√5 + 2
Why is this the correct answer?
Rationalization removes a radical from a denominator by multiplying the numerator and denominator by the denominator’s conjugate. The conjugate of √5 − 2 is √5 + 2. Therefore, 1/(√5 − 2) = (√5 + 2)/[(√5 − 2)(√5 + 2)]. Applying the difference-of-squares identity gives the denominator 5 − 4 = 1, so the fraction simplifies to √5 + 2. Hence option A is correct. Option B is merely the original denominator expression and does not rationalize the fraction. Option C introduces an unsupported factor of 9, while option D is not equivalent to the original fraction. The essential step is choosing the conjugate, which converts the radical denominator into a rational number.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Irrational numbers.
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