√201 – √199
(√201 – √199) × [(√201 + √199/ (√201 + √199)]
(201 – 199) / (√201 + √199)
2/(√201 + √199)
Similarly,
√401 – √399
(√401 – √399) × [(√401 + √399 / (√401 + √399)]
(401 – 399) / (√401 + √399)
2/ (√401 + √399)
Similarly,
√101 – √99
(√101 – √99) × [(√101 + √99) / (√101 + √99)]
(101 – 99)/ (√101 + √99)
2/ (√101 + √99)
Similarly,
√301 – √299
(√301 – √299) × [(√301 + √299) / (√301 + √299)]
(301 – 299) / (√301 + √299)
2/(√301 + √299)
As we know,
If numerator are same, then the fraction which has largest denominator, has minimum value.
So, the smallest = √401 – √399
Short Trick:
Sum of which function is greater, lesser the value.
√201 – √199 ⇒ 201 + 199 = 400
√401 – √399 ⇒ 401 + 399 = 800
√101 – √99 ⇒ 101 + 99 = 200
√301 – √299 ⇒ 301 + 299 = 600
Sum of √401 – √399 is greater so we can say this is the smallest in among.