Question

Write square numbers and cube numbers from 1 to 30 natural numbers.

Answer 1

Hint: To obtain the square and cube of numbers from 1 to 30 we will use squaring and cubing method. Firstly we will write down all the numbers from 1 to 30 which are natural. Then we will form a table where we will write the square of all the numbers by multiplying each number by itself. Finally we will form another table where we will multiply each number thrice and hence get our desired answer.

Complete step-by-step solution:
So we have to find the square numbers and cube numbers from 1 to 30.
So we have the following number from 1 to 30 which are natural numbers.
$1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30$
Now we will form a table where we will get the square of each number by multiplying it by itself.

Numbers	Square of numbers
1	$1\times 1=1$
2	$2\times 2=4$
3	$3\times 3=9$
4	$4\times 4=16$
5	$5\times 5=25$
6	$6\times 6=36$
7	$7\times 7=49$
8	$8\times 8=64$
9	$9\times 9=81$
10	$10\times 10=100$
11	$11\times 11=121$
12	$12\times 12=144$
13	$13\times 13=169$
14	$14\times 14=196$
15	$15\times 15=225$
16	$16\times 16=256$
17	$17\times 17=289$
18	$18\times 18=324$
19	$19\times 19=361$
20	$20\times 20=400$
21	$21\times 21=441$
22	$22\times 22=484$
23	$23\times 23=529$
24	$24\times 24=576$
25	$25\times 25=625$
26	$26\times 26=676$
27	$27\times 27=729$
28	$28\times 28=784$
29	$29\times 29=841$
30	$30\times 30=900$

Next we will find the cube of all numbers i.e. multiplied three times by itself as below:

Numbers	Cube of numbers
1	$1\times 1\times 1=1$
2	$2\times 2\times 2=8$
3	$3\times 3\times 3=27$
4	$4\times 4\times 4=64$
5	$5\times 5\times 5=125$
6	$6\times 6\times 6=216$
7	$7\times 7\times 7=343$
8	$8\times 8\times 8=512$
9	$9\times 9\times 9=729$
10	$10\times 10\times 10=1000$
11	$11\times 11\times 11=1331$
12	$12\times 12\times 12=1728$
13	$13\times 13\times 13=2197$
14	$14\times 14\times 14=2744$
15	$15\times 15\times 15=3375$
16	$16\times 16\times 16=4096$
17	$17\times 17\times 17=4913$
18	$18\times 18\times 18=5832$
19	$19\times 19\times 19=6859$
20	$20\times 20\times 20=8000$
21	$21\times 21\times 21=9261$
22	$22\times 22\times 22=10648$
23	$23\times 23\times 23=12167$
24	$24\times 24\times 24=13824$
25	$25\times 25\times 25=15625$
26	$26\times 26\times 26=17576$
27	$27\times 27\times 27=19683$
28	$28\times 28\times 28=21952$
29	$29\times 29\times 29=24389$
30	$30\times 30\times 30=27000$

So we got the square and cube of 1 to 30 natural numbers as 1,4,9,16,25,36,49,64,81,100,121,144,169,
196,225,256,289,324, 361,400,441,484,529,576,625,676,729,784,841,900 and 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 15625, 17576, 19683, 21952, 24389, 27000 respectively

Note: Square of a number means multiplying the number by itself and if we have to find the square root we divide the power of the number into half. Cube of a number is multiplying the number three times by itself and the cube root is dividing the power of the number by 3. A perfect square is the one whose square root is a natural number and a perfect cube is the one whose cube root is a natural number.