# The cube root of thrice a number is equal to the cube root of 144 more than the number. What is the number?

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The number is 72. I have no solutions because I don't know how to solve it systematically. I have done it using trial and error.

1 x 1 x 1 = 1

2 x 2 x 2 = 8

3 x 3 x 3 = 27

4 x 4 x 4 = 64

5 x 5 x 5 =125

6 x 6 x 6 = 216

7 x 7 x 7 =343

8 x 8 x 8 = 512

9 x 9 x 9 =729

1 - 144 = negative number and has no cube root, therefore, 1 is not the number.

8 - 144 = negative number and has no cube root, therefore, 8 is not the number.

27 - 144 = (the same)

64 - 144 = (the same)

125 - 144 = (the same)

216 - 144 = 72, the answer is positive, therefore, 72__could be__ the number.

343 - 144 = 199, the answer is positive, therefore, 199__could be__ the number.

512 - 144 = 368, the answer is positive, therefore, 368__could be__ the number.

729 - 144 = 585, the answer is positive, therefore, 585__could be__ the number.

The numbers left that we can try are: 199, 368, 585, 72

Let us try:

199 x 3 = 597, the cube root of 597 is an irrational number, it is not the answer.

368 x 3 =1,104, the cube root of 1,104 is complicated, it is not the answer.

585 x 3 = 1, 755, the cube root of 1, 755 is complicated, it is not the answer.

72 x 3 = 216, the cube root of 216 is 6, 72__could be__ the answer.

The number left, survived, and passed the previous screening is 72.

Let us try it:

=

6 = 6 , it is equal, CORRECT!!!

Therefore, the number is 72.

1 x 1 x 1 = 1

2 x 2 x 2 = 8

3 x 3 x 3 = 27

4 x 4 x 4 = 64

5 x 5 x 5 =125

6 x 6 x 6 = 216

7 x 7 x 7 =343

8 x 8 x 8 = 512

9 x 9 x 9 =729

1 - 144 = negative number and has no cube root, therefore, 1 is not the number.

8 - 144 = negative number and has no cube root, therefore, 8 is not the number.

27 - 144 = (the same)

64 - 144 = (the same)

125 - 144 = (the same)

216 - 144 = 72, the answer is positive, therefore, 72

343 - 144 = 199, the answer is positive, therefore, 199

512 - 144 = 368, the answer is positive, therefore, 368

729 - 144 = 585, the answer is positive, therefore, 585

The numbers left that we can try are: 199, 368, 585, 72

Let us try:

199 x 3 = 597, the cube root of 597 is an irrational number, it is not the answer.

368 x 3 =1,104, the cube root of 1,104 is complicated, it is not the answer.

585 x 3 = 1, 755, the cube root of 1, 755 is complicated, it is not the answer.

72 x 3 = 216, the cube root of 216 is 6, 72

The number left, survived, and passed the previous screening is 72.

Let us try it:

=

6 = 6 , it is equal, CORRECT!!!

Therefore, the number is 72.