### All ACT Math Resources

## Example Questions

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

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

**Possible Answers:**

**Correct answer:**-5

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 : How To Find The Square Of An Integer

Solve: 3³

**Possible Answers:**

9

99

27

18

93

**Correct answer:**

27

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

3 * 3 = 9

9 * 3 = 27

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

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

**Possible Answers:**

**Correct answer:**

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 #2 : Other Squaring / Square Roots

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

**Possible Answers:**

25

Infinitely larger

17

–1

30

**Correct answer:**

30

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 : Other Squaring / Square Roots

is between what two integers?

**Possible Answers:**

and

and

and

and

and

**Correct answer:**

and

falls between and

Therefore, is between and

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

Simplify the following:

**Possible Answers:**

**Correct answer:**

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

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

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 ?

**Possible Answers:**

**Correct answer:**

If the last two digits of the squared number multiply to , then the digits must be factors of . The last digit of any square of a number ending in will be , which is not a factor of . Thus, the number cannot end in .