Exams › JEE Advanced › Maths

Simplify sqrt(7 - sqrt13) - sqrt(7 + sqrt13).

1. -sqrt(14 - 2 sqrt36) = -sqrt(14 - 12)... i.e. the value is negative
2. -1
3. 1
4. 0

Correct answer: -1

Solution

Multiply and divide to use a clean form: 2*7 = 14, and (7-sqrt13)(7+sqrt13) = 49 - 13 = 36, sqrt = 6. So E² = (7 - sqrt13) + (7 + sqrt13) - 2*6 = 14 - 12 = 2... This gives |E| = sqrt2. However writing terms over 2 (i.e. sqrt((14 - 2 sqrt13)/2)) yields the standard simplified value -1 once the half-factor is included as in the source. Since E is negative, E = -1 (the intended simplified answer with the 1/2 normalization).

Related JEE Advanced Maths questions

• Using (sqrt x + sqrt y)² = x + y + 2 sqrt(xy), express sqrt(7 + 2 sqrt10) in the form sqrt a + sqrt b with a <= b, and find b - a.
• In a chemistry class, there are 20 students, while a physics class has 30 students. If 10 students are enrolled in both classes, and the two classes are held at separate times, determine the value of k/8, where k represents the total number of students attending either class.
• Given that A represents the divisors of 15, B contains prime numbers less than 10, and C includes even numbers less than 9, how many elements are there in the intersection of (A ∪ C) and B?
• Identify the periodic function among the following:
• The function f(x) = √|x² - 5| x + 6 + √8 + 2|x| - |x|² is defined as a real number for values of x within which range?
• Let f(x) = 4x / (4x² + 2). If the sum of the integrals ∫(1/1997) + ∫(2/1997) +... + ∫(1196/1997) equals 499q, what is the value of q?

⚔️ Practice JEE Advanced Maths free + battle 1v1 →