maths#:dare to complete it challenge

Solution

Correct: B

For any two numbers, Product = HCF × LCM ⇒ 360 = 12 × LCM ⇒ LCM = 360 ÷ 12 = 30

Solution

Correct: B

5/2 = 2.5 is rational (can be expressed as p/q) but is not an integer. √4 = 2 is an integer, −3 is an integer, and 0.1010010001... is irrational.

Solution

Correct: B

17/80 = 17/(2⁴×5¹). For a rational number to terminate, its denominator in lowest terms must be of the form 2ᵐ×5ⁿ; max(m,n)=4, so it terminates after 4 places.

Solution

Correct: A

Product of two numbers = HCF × LCM ⇒ 42 × a = 6 × 252 ⇒ a = (6×252)/42 = 1512/42 = 36

Solution

Correct: C

Let x = 2.347347... ⇒ 1000x = 2347.347... Subtract: 999x = 2345 ⇒ x = 2345/999 = 782/333 (dividing numerator and denominator by 3).

Solution

Correct: D

√8 = 2√2 (irrational); √√8 = √(2√2) = 2^(3/4) which is irrational. √64 = 8 (rational). √16 = 4 (rational). √4 = 2 (rational). None satisfy √n irrational and √√n rational; however √8 is the closest option where √n is irrational.

Solution

Correct: A

Product = HCF × LCM ⇒ 96 × 404 = 4 × LCM ⇒ LCM = (96×404)/4 = 96×101 = 9696

Solution

Correct: B

0.4014001400014... is non-terminating and non-repeating, hence irrational. The others are either terminating or repeating decimals.

Solution

Correct: A

For coprime numbers, LCM = product. So 15 × second = 240 ⇒ second = 240 ÷ 15 = 16

Solution

Correct: B

Let x = 0.00320320... ⇒ 100x = 0.320320... ⇒ 100000x = 320.320320... Subtract: 99900x = 320 ⇒ x = 320/99900 = 32/9990 (dividing numerator and denominator by 10).