Question

If 52272 = p²×q³×r⁴ where p, q and r are prime numbers, then the value of (2p+ q-r) is
(1) 23
(2) 29
(3) 21
(4) 22

Answer 1

answer : option (4) 22

explanation : it is given that, 52272 = p²×q³×r⁴ where p, q and r are prime numbers.

first of all, we should write prime factors of 52272

so, prime factors of 52272 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 11 × 11

= 2⁴ × 3³ × 11²

= 11² × 3³ × 2⁴

but given 52272 = p² × q³ × r⁴

on comparing , we get

p = 11 , q = 3 and r = 2

[ also you can see that 11 , 3 and 2 are prime numbers . ]

now value of (2p + q - r) :

= 2 × 11 + 3 - 2

= 22 + 3 - 2

= 24 - 2

= 22