Other Squaring / Square Roots - ACT Math
Card 0 of 7
If (x - 3)2 = 64, what is a possible value of x?
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.
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.
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When you square the following numbers, which one results in an irrational number?
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.
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.
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How much larger is the sum of the squares of –2, –3, and 4 than the sum of these integers?
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
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
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Solve: 3³
Solve: 3³
When using a cube root. 3³ becomes 3 * 3 * 3.
3 * 3 = 9
9 * 3 = 27
When using a cube root. 3³ becomes 3 * 3 * 3.
3 * 3 = 9
9 * 3 = 27
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is between what two integers?
falls between 
and 
Therefore, 
is between 
and 
Therefore,
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Simplify the following: 
Simplify the following:
is the same as 
multiplied by 
. Thus, the answer is 
.
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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 
?
The last two digits in the square of a number
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 
.
If the last two digits of the squared number multiply to
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