ACT Math · Number operations and exponents
Which expression is equivalent to 43+√(5) with a rationalized denominator?
Which expression is equivalent to with a rationalized denominator?
Answer and explanation
Answer: F: 3 - √(5)
Multiply numerator and denominator by the conjugate, 3−√5: [4(3−√5)]/[(3+√5)(3−√5)] = [4(3−√5)]/[9−5] = [4(3−√5)]/4 = 3−√5. Choice J stops one step early, reporting the numerator's expansion without dividing by the denominator's simplified value of 4.
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