1. Find Least number of 4 digits which is a perfect Square

Solution:
Least number of 4 digits = 1000

	3	1
3	10	00
	9
61	1	00
		61
62		39

 
Number = 1000
Square Root = 31

Here, Quotient = 31, Remainder = 39

`:.` Number to be added

`= 2 xx "Quotient" - "Remainder" + 1`

`= 2 xx 31 - 39 + 1`

`=24`

`:.` Perfect square number `=1000 + 24=1024`

`:. sqrt(1024)=32`

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2. Find Greatest number of 5 digits which is a perfect Square

Solution:
Least number of 5 digits = 99999

	3	1	6
3	9	99	99
	9
61		99
		61
626		38	99
		37	56
632		1	43

 
Number = 99999
Square Root = 316
`:.` Number to be substracted = 143

`:.` Perfect square number = 99999 - 143=99856

`:. sqrt(99856)=316`

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3. Find Greatest number of 5 digits which is a perfect Cube

Solution:
Least number of 5 digits = 99999

	4	6
16	99	999
	64
5556	35	999		`300 xx 4^2 + 30 xx 4 xx 6 + 6^2=4800 + 720 + 36=5556`
	33	336
---	2	663

 
Number = 99999
Cube Root = 46

`:.` Number to be substracted = 2663

`:.` Perfect cube number = 99999 - 2663=97336

`:. root (3)(97336)=46`

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4. Find Least number of 6 digits which is a perfect Square

Solution:
Least number of 6 digits = 100000

	3	1	6
3	10	00	00
	9
61	1	00
		61
626		39	00
		37	56
632		1	44

 
Number = 100000
Square Root = 316

Here, Quotient = 316, Remainder = 144

`:.` Number to be added

`= 2 xx "Quotient" - "Remainder" + 1`

`= 2 xx 316 - 144 + 1`

`=489`

`:.` Perfect square number `=100000 + 489=100489`

`:. sqrt(100489)=317`

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