All ACT Math Resources
Example Question #1 : How To Find The Square Of An Integer
If (x - 3)2 = 64, what is a possible value of x?
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 : Other Squaring / Square Roots
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?
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 #3 : 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?
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 #62 : Basic Squaring / Square Roots
is between what two integers?
falls between and
Therefore, is between and
Example Question #4 : How To Find The Square Of An Integer
Simplify the following:
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 ?
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 .