Square Roots + Perfect Squares
What is a perfect square?
A number that is the product of a number and itself
What are the two closest perfect squares surrounding 20?
16 (42) and 25 (52)
Evaluate if x = 10:
4x - 5
35
Write an expression and evaluate for a = 65:
"Your aunt's age, a, minus 25 years"
a - 25
40 years
Define "square root."
A square root is the factor that produces a square number when you multiply it by itself; the "opposite" of squaring a number
What is the square root of 121?
11
5 and 6
Evaluate if x = 13
4x - 5
Write an expression and evaluate for s = 60
"the number of seashells, s, divided by 10"
s/10
6
List the five perfect squares between 0 and 36.
1, 4, 9, 16, 25
What is the square root of 225?
15
The square root of 101 is closest to what integer?
10
Evaluate if x = 7 and y = -5:
3x - 6y
51
Write an expression and evaluate for t = 5 bags of Takis.
"You spend $3 on each bag of Takis, t, and an additional $5 for a drink."
3t + 5
$20 total
List the three perfect squares between 36 and 100.
49, 64, 81
The sum of two perfect squares is 61. What are the two perfect squares?
25 and 36
The square root of 90 is between what two integers, and closest to which one of those two?
Between 9 and 10, closer to 9
Evaluate if x = -6 and y = -10
4.5x - 17y + 12
155
Write an expression and evaluate for m = 20 miles walked.
"For a community walk-a-thon, your sponsor donates a flat fee of $5 upfront, plus an additional $2 for each mile that you walk."
2m + 5
$45 earned
Write an expression and evaluate for m = 10 months.
"Your cellphone plans costs $40 per month on top of a $35 activation fee."
40m + 35
$435 total
The sum of two perfect squares is 269. What are the square roots of those two perfect squares?
10 and 13 (100 and 169)
Explain the process for estimating the square root of a number that is not a perfect square.
Look for the perfect squares that are closest to your target number, above and below. Find the square roots of those perfect squares to see what integers you will be between. Whichever perfect square is closer to your original number, take its square root, and that's the integer that your square root will be closest to. (For example, since 35 is closer to 36 than 25, the square root of 35 is closest to the integer 6.)
Evaluate if x = 4, y = 12, and z = -20:
-5x + 2y - 0.5z
14
Write an expression and evaluate for f = 32 friends.
"For an upcoming party, you order 12 pizzas. If each pizza has 8 slices, how many slices does each person get if you invite f friends and everyone gets the same amount?"
(12*8)/f
3 slices per person
The square root of 405 is between which two integers? Which integer is is closest to?
Between 20 and 21, closer to 20