Let me list some perfect square numbers for you that may be helpful.
0*0 = 0
1*1 = 1
2*2 = 4
3*3 = 9
4*4 = 16
5*5 = 25
6*6 = 36
7*7 = 49
8*8 = 64
9*9 = 81
10*10 = 100
11*11 = 121
12*12 = 144
13*13 = 169
You want to know between which 2 whole numbers does sqrt(138) lie.
sqrt(138) is asking, what number times itself gives me 138.
138 is larger than 121 (11*11) and smaller than 144 (12*12). This tells me that sqrt(138) lies somewhere between 11 and 12.
between which two consecutive integers does the square root lie 123
9 and 10
The square root of 73 is between 8 and 9.
31-32
14 and 15
The square root of 47 lies between the consecutive whole numbers 6 and 7.
between which two consecutive integers does the square root lie 123
The square root is between 5 and 6.
9 and 10
2 and 3
9 and 10
The square root of 73 is between 8 and 9.
The square root of 14 lies between 3 and 4.
5.385 is the square root of 29. No consecutive numbers.
The numbers are 88 and 89 (88 x 89 = 7,832). This is very easy to find. The products you are looking for are consecutive and so they are very close to each other. Calculate the square root of the number, and it is easy to see that if there are two consecutive whole numbers that will be products of the number, they will be consecutive whole numbers very close to the square root. The square root of 7832 is about 88.5.
31-32
14 and 15