Exams › JEE Main › Maths

Without computing the decimal values of sqrt(3) and sqrt(14), determine which of the two numbers 5 + sqrt(3) and 3 + sqrt(14) is greater.

1. 5 + sqrt(3)
2. 3 + sqrt(14)
3. They are equal
4. Cannot be determined

Correct answer: 3 + sqrt(14)

Solution

Subtract 3 from both: compare 2 + sqrt(3) with sqrt(14). Both positive, so square: (2 + sqrt(3))² = 4 + 4sqrt(3) + 3 = 7 + 4sqrt(3) versus 14. Compare 4sqrt(3) with 7 by squaring: 16*3 = 48 versus 49. Since 48 < 49, 4sqrt(3) < 7, so 7 + 4sqrt(3) < 14, meaning 2 + sqrt(3) < sqrt(14), thus 5 + sqrt(3) < 3 + sqrt(14). Therefore 3 + sqrt(14) is the greater number.

Related JEE Main Maths questions

• Let A be the set {(n, 2n): n ∈ N} and let B be the set {(2n, 3n): n ∈ N}. What is the intersection A ∩ B?
• Let set A contain 3 elements and set B contain 6 elements. Then the cardinality of their union must satisfy
• Given the sets A = {1, 2, 5} and B = {3, 4, 5, 9}, what is A ∩ B?
• At a conference with 100 attendees, 29 are Indian women and 23 are Indian men. Among the Indian attendees, 4 are doctors, and 24 are either men or doctors. If there are no foreign doctors, how many foreigners and how many women doctors are present at the conference?
• Let X and Y be two non-empty sets, and let A be a non-empty set such that X ∩ A = Y ∩ A = A and X ∪ A = Y ∪ A. Which of the following must be true?
• If A and B are non-empty sets with A containing B, then which of the following is true?

⚔️ Practice JEE Main Maths free + battle 1v1 →