- AIIMS Bhuvneshwar NO- 2018

AIIMS Bhuvneshwar NO- 2018

Non Nursing Subjects

Hard

Appeared in: AIIMS Bhuvneshwar NO- 2018

Explanation

The core of the problem is to rationalize the denominator of the fraction (3 + √5) / (3 - √5) by multiplying both the numerator and denominator by the conjugate of the denominator, which is (3 + √5).
Simplifying the numerator gives (3 + √5)² = 9 + 6√5 + 5 = 14 + 6√5.
Simplifying the denominator gives (3 - √5)(3 + √5) = 3² - (√5)² = 9 - 5 = 4.
The expression simplifies to (14 + 6√5) / 4, which is 7/2 + (3/2)√5.
By comparing this to a + b√5, we find a = 7/2 and b = 3/2.
The final step is to calculate a + b, which is 7/2 + 3/2 = 10/2 = 5.

Option A: The value 7 is incorrect. This might be obtained by mistakenly taking only the value of 'a' after dividing the rational part of the numerator by 2 (i.e., 14/2), but ignoring 'b'.
Option B: The value 10 is incorrect. This error could arise if one incorrectly calculates a+b as 7+3=10, forgetting that both 'a' and 'b' have a denominator of 2.
Option C: The value 8 is incorrect. There is no clear arithmetic error that leads to this result, suggesting it is likely a random distractor or the result of multiple calculation mistakes.

Visual 1: Infographic: A visual guide showing the key algebraic identities used in this problem: (x+y)² = x² + 2xy + y² and (x-y)(x+y) = x² - y², along with a step-by-step breakdown of the rationalization process.

Clinical Relevance

Nursing practice connection: Knowing Rationalization of surds and simplification of algebraic expressions helps nurses interpret findings accurately and avoid errors in routine assessment, medication administration, and patient teaching.
This is a mathematical aptitude question, designed to test numerical ability and problem-solving skills, which are essential for nurses in tasks like dosage calculations and data interpretation.
While this specific problem on surds does not have a direct clinical application, the underlying skills in logical, step-by-step problem-solving are transferable to clinical decision-making.
What if the question was (3 - √5) / (3 + √5)? The process would be similar, but the conjugate would be (3 - √5). This would lead to a = 7/2 and b = -3/2, making a+b = (7-3)/2 = 2.

How to Approach the Question

First, identify the type of problem. This is an algebra question involving surds (expressions with roots).
Recognize that the fraction on the left needs to be simplified to match the format on the right.
The key technique for simplifying a fraction with a binomial surd in the denominator is 'rationalization'.
Multiply the numerator and denominator by the conjugate of the denominator. The conjugate of (x - y) is (x + y).
Carefully apply the algebraic identities (a+b)² and (a-b)(a+b) to expand the numerator and denominator.
Simplify the resulting expression and separate it into its rational and irrational parts to find the values of 'a' and 'b'.

Concept Tested & Keywords

Concept Tested: Rationalization of surds and simplification of algebraic expressions.
Stem keywords: (3+√5)/(3-√5), a + b√5, a + b
Lead-in keywords: is equal to

QxTJ0-Fq69K6iMxNH1tniA

Practise the full AIIMS Bhuvneshwar NO- 2018

Attempt every question from this paper in a timed mock, then review the full solution for each one.