# ACT Math : How to find the square of an integer

## Example Questions

### Example Question #1 : Other Squaring / Square Roots

If (x - 3)2 = 64, what is a possible value of x?

-8
-5
5
10
8
Explanation:

In order to solve for x, we must first take the square root of both sides.

(x - 3)2 = 64

(x - 3) = +/- 8

The square root of 64 is either 8 or -8. We then solve the equation with both possible values of the square root of 64.

x - 3 = 8 (Add 3 to both sides.)

x = 11

x - 3 = -8 (Add 3 to both sides.)

x = -5

x = 11 or -5. -5 is the only possible value of x that is an answer choice.

### Example Question #1 : Other Squaring / Square Roots

Solve: 3³

27

93

9

99

18

27

Explanation:

When using a cube root. 3³ becomes 3 * 3 * 3.

3 * 3 = 9

9 * 3 = 27

### Example Question #62 : Basic Squaring / Square Roots

When you square the following numbers, which one results in an irrational number?

Explanation:

A rational number is any number than can be expressed as a fraction or a quotient of two integers. The square of π is still an irrational number. (√(2))2 = 2, (1/3)2 = 1/9, (7/17)2 = 49/289, (1/2)2 = 1/4, all can be writen in fractional form, and are thus, rational numbers.

### Example Question #1 : How To Find The Square Of An Integer

How much larger is the sum of the squares of –2, –3, and 4 than the sum of these integers?

25

Infinitely larger

30

17

–1

30

Explanation:

The square of –2 is 4, of –3 is 9, and of 4 is 16.

The sum of these squares is 29.

The sum of (–2) + (–3) + (4) is –1.

29 – (–1) = 30

### Example Question #2 : How To Find The Square Of An Integer

is between what two integers?

and

and

and

and

and

and

Explanation:

falls between  and

Therefore,  is between  and

### Example Question #65 : Basic Squaring / Square Roots

Simplify the following:

Explanation:

is the same as  multiplied by . Thus, the answer is .

### Example Question #66 : Basic Squaring / Square Roots

The last two digits in the square of a number  have a product of . Which of the following could NOT be the last digit of ?