ACT Math : How to find the square of an integer

Study concepts, example questions & explanations for ACT Math

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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:
10
-8
5
-5
8
Correct answer: -5
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 #2 : How To Find The Square Of An Integer

Solve: 3³

Possible Answers:

27

99

93

18

9

Correct answer:

27

Explanation:

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

3 * 3 = 9

9 * 3 = 27

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

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

Possible Answers:

Correct answer:

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 #86 : Arithmetic

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

Possible Answers:

17

25

Infinitely larger

–1

30

Correct answer:

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 #3 : How To Find The Square Of An Integer

 \dpi{100} \small \sqrt{15} is between what two integers?

Possible Answers:

\dpi{100} \small 3 and \dpi{100} \small 4

\dpi{100} \small 2 and \dpi{100} \small 3

\dpi{100} \small 5 and \dpi{100} \small 6

\dpi{100} \small 7 and \dpi{100} \small 8

\dpi{100} \small 4 and \dpi{100} \small 5

Correct answer:

\dpi{100} \small 3 and \dpi{100} \small 4

Explanation:

\dpi{100} \small 3\times 3=9

\dpi{100} \small 4\times 4=16

 falls between  and  

Therefore, \dpi{100} \small \sqrt{15} is between  and  

Example Question #4 : How To Find The Square Of An Integer

Simplify the following: 

Possible Answers:

Correct answer:

Explanation:

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

Example Question #5 : 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:

Explanation:

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 .

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