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The Square Root cycle

WE all often come around mathematical problems where we have to find the square roots of numbers. But has anyone noticed a cyclic occurence in their
answers? Well,let us see this cycle:-

1.First let us find the square root of 1 i.e. 1.
2.Now, let us find the square root of 4 i.e. 2.
3.Now subtract 1 from 4,so as to obtain 3.
4.Now add 4 and the next odd number to 3,5 to get 9.
5.WE can see that 3 is the square root of 9.
6.Now add the next odd number to 5,7 to 9 to get 16(which has the square root as 4 )
In this way,a cycle can be observed in these numbers.

Here are some more examples:-

5x5=16+9=25
6x6=25+11=36
7x7=36+13=49
8x8=49+15=64
9x9=64+17=81
10x10=81+19=100
11x11=100+21=121
12x12=121+23=144
13x13=144+25=169
14x14=169+27=196
15x15=196+29=225
16x16=225+31=256
17x17=256+33=289
18x18=289+35=324
19x19=324+37=361
20x20=361+39=400
21x21=400+41=441
22x22=441+43=484
23x23=484+45=529
24x24=529+47=576
25x25=576+49=625

Vedant Pathak

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