Exams › JEE Main › Maths

Simplify: (i) ((5*sqrt(3) + sqrt(50))*(5 - sqrt(24))) / (sqrt(75) - 5*sqrt(2)) (ii) (3*sqrt(2))/(sqrt(6) + sqrt(3)) - (4*sqrt(3))/(sqrt(6) + sqrt(2)) + (sqrt(6))/(sqrt(3) + sqrt(2))

1. (i) 1; (ii) 0
2. (i) 0; (ii) 1
3. (i) sqrt(2); (ii) sqrt(3)
4. (i) 5; (ii) -1

Correct answer: (i) 1; (ii) 0

Solution

Part (i) simplifies because (5*sqrt(3) + 5*sqrt(2)) is a multiple of (sqrt(75) - 5*sqrt(2))'s structure once you account for sqrt(24) = 2*sqrt(6). Part (ii) telescopes to zero after rationalizing.

Related JEE Main Maths questions

• Rationalize the denominator of 1/(3*sqrt(2) + sqrt(5)) and choose the simplified form.
• Find rational numbers a and b such that (2 + 3 sqrt(5)) / (1 - 3 sqrt(5)) = a + b sqrt(5).
• 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?

⚔️ Practice JEE Main Maths free + battle 1v1 →