We are also memorizing this, and we need to memorize Pythagorean theorem. Let me tell you the square of 1 ~ 50 by omitting the exponent.

1= 1

2=4

3=9

4= 16

5=25

6=36

7=49

8=64

9=8 1

10= 100

1 1= 12 1

12= 144

13= 169

14= 196

15=225

16=256

17=289

18=324

19=36 1

20=400

2 1=44 1

22=484

23=529

24=576

25=625

26=676

27=729

28=78 1

29=84 1

30=900

3 1=96 1

32= 1024

33= 1089

34= 1 156

35= 1225

36= 1296

37= 1369

38= 1444

39= 152 1

40= 1600

4 1= 168 1

42= 1764

43= 1849

44= 1936

45=2025

46=2 1 16

47=2209

48=2304

49=240 1

50=2500

I hope it helps you!