Number Classifications (no calculator)
Which subset(s) of the number system does sqrt(100) belong to?
Identify any of the following that apply:
Natural, Integer, Rational, Irrational, Real, Non-real
Natural, Integer, Rational, Real
Insert <, > or = to make the statement true.
sqrt(49) 21/3
sqrt(49) = 7
21/3 = 7
sqrt(49) = 21/3
Between which two consecutive whole numbers does sqrt(30) lie? Explain how you know.
Closest perfect square below 30 is 25. Closest perfect square above 30 is 36. sqrt(25) = 5 and the sqrt(36) = 6 .
Therefore sqrt(3) must lie between 5 and 6 .
Convert sqrt(20) into lowest equivalent radical form. Show all your steps.
sqrt(20) = sqrt(4) xx sqrt(5) = 2 xx sqrt(5) = 2sqrt(5)
NO CALCULATOR
A tech startup begins with 5 users on Day 1. The number of users quintuples (5x) each day. Write a power expression to represent the number of users on Day 4.
Number of users on Day 4 = 5^4
Is the number 43/7 rational, irrational or non-real? Explain why.
Rational (and real). The number is written as a fraction of two integers.
Insert <, > or = to make the statement true.
2^4 - 5 |-15|
2^4 - 5 = 16 - 5 = 11
|-15| = 15
2^4 - 5 < |-15|
Estimate sqrt(30) to the tenths place and explain your reasoning.
Approximately 5.5. 30 is approximately halfway between 25 and 36. Therefore the square root of 30 should fall approximately halfway between the square root of 15 (5) and the square root of 36 (6).
Convert sqrt(45) into lowest equivalent radical form. Show all your work.
sqrt(45) = sqrt(9) xx sqrt(5) = 3 xx sqrt(5) = 3sqrt(5)
NO CALCULATOR
A bacteria culture starts with 2 cells and doubles at every hour. Write a power expression for the number of bacteria cells at Hour 5. Then evaluate the power expression and use a therefore statement to state the total number of bacteria cells in the culture at Hour 5.
Number of bacteria at Hour 5 = 2^5 = 32
Therefore, there are 32 bacteria cells in the culture at Hour 5.
Classify the expression -sqrt(11) - is it rational or irrational? Explain why.
Irrational, because it is a non-repeating, non-terminating decimal.
Insert <, > or = to make the statement true.
|-20| / sqrt(25) 2^3 - 3
|-20|/sqrt(25) = 20/5 = 4
2^3 - 3 = 8 - 3 = 5
|-20|/sqrt(25) < 2^3 - 3
Estimate sqrt(80) to the tenths place and explain your reasoning.
Approximately 8.9. The square root of 64 is 8. The square root of 81 is 9. 80 is much closer to 81 than 64. Therefore the square root of 80 will be between the square root of 64 (8) and the square root of 81 (9), but much closer to the square root of 81.
Convert sqrt(50) into lowest equivalent radical form. Show all your work.
sqrt(5) = sqrt(25) xx sqrt(2) = 5 xx sqrt(2) = 5sqrt(2)
CALCULATOR PERMITTED
A square art gallery has a total area of 225 m^2 . Write an expression using a square root to represent the length of one side wall. Then evaluate the expression and use a therefore statement to state the length of the side wall.
sqrt(225) = 15
Therefore, the side length of the side wall is 15 m
To which classification does sqrt(-100) belong and why?
Non-real. The square root of a negative number is not a real number.
Insert <, > or + to make the statement true.
sqrt(81) - 3^2 0.5 xx 4
sqrt(81) - 3^2 = 9 - 9 = 0
0.5 x 4 = 2
sqrt(81) - 3^2 < 0.5 xx 4
Estimate sqrt(130) to the tenths place. Explain your reasoning.
Approximately 11.4. The square root of 121 is 11. The square root of 144 is 12. 130 is 9 away from 121 and 14 away from 144. Therefore the square root of 130 will fall between the square root of 121 (11) and 144 (2) but be slightly closer to the square root of 121.
Convert sqrt(72) into lowest equivalent radical form. Show all your work.
sqrt(72) = sqrt(36) xx sqrt(2) = 6 xx sqrt(2) = 6sqrt(2)
CALCULATOR PERMITTED
A square park has an area of 324 m^2 . If a fence goes around the entire park, how long is the fence? Express your final answer using a therefore statement and remember to include units.
sqrt(324) = 18
side length = 18
perimeter 18 xx 4 = 72
Therefore the fence is 72 m long.
Classify 0.4 bar 6 and -(3^4) . Which subset(s) of the number system do they belong to? Explain why.
0.4 bar 6 is rational and real because it is a repeating decimal. All repeating decimals are rational numbers and all rational numbers are real numbers.
-(3^4) = -81 which is an integer, rational and real number.
Order the following numbers from LEAST to GREATEST using <.
pi - 7/4 sqrt(15) -2.8 |-3|
Decimal equivalents: -2.8 < -1.75 < 3 < 3.1416 < 3.9
-2.8 < - 7/4 < |-3| < pi < sqrt(15)
Estimate sqrt(18) to the tenths place and state the two consecutive whole numbers it will fall between. Explain your reasoning.
Convert sqrt(147) into lowest equivalent radical form. Show all your work.
sqrt(147) = sqrt(49) xx sqrt(3) = 7 xx sqrt(3) = 7sqrt(3)
CALCULATOR PERMITTED
In a computer game, the enemy population quadruples (4x) at each level. Level 1 starts with 4 enemies. Write a general power expression for the size of the enemy population at any given level, L. What is the first level where there are more than 1,000 enemies? How many enemies are in that level? Remember to show all your work, state your final answer using a therefore statement and include any necessary units.
Number of enemies at level, L 4^L
4^4 = 256 4^5 = 1024
Therefore Level 5 is the first level with over 1,000 enemies. There are 1024 total enemies in Level 5.