Rational vs Irrational Numbers
Rachel says that the square root of 49 is rational. Sonya says that the cube root of 49 is rational. Who is correct and why?
Rachel is correct because it is a whole number and can be written as a fraction.
Approximate the square root of 70. Between what two whole numbers must the square root of 70 lie?
8 and 9
Which value is equivalent to (54)4?
A. 50
B. 54
C. 516
D. 58
C. 516
What is x3= 1/27?
1/3
What is 2 x 10-7 written in standard notation?
0.0000002
The value of pi cannot be written as the ratio of two integers. Which statement is true?
A. pi is a rational number.
B. The decimal expansion of pi terminates.
C. pi is an irrational number.
D. The decimal expansion of pi repeats.
C. pi is an irrational number
No because is greater than 4 and less than 5.
Which expressions are equivalent to 28?
A. 2-4*2-2
B. 1/2-8
C. (2-4)-2
D. 2-5*2-3
E. (2-10*21)-3
BC
Solve.
x2= 625
25 and -25
6 x 10 4
Which of the following is correct? Select three that apply.
A. 0.618 with the 618 repeating = 68/111
B. 0.1234 with the 4 repeating = 1111/9000
C. 0.54 with the 54 repeating = 6/11
D. 0.83 with the 83 repeating = 5/6
E. 0.4 repeating = 4/9
BCE
Janice has a square garden with an area of 247 square feet. What is the approximate length of one side of the garden? Round to the nearest hundredth.
15.72
The approximate population of Michigan is 97.The approximate population of South Dakota is 95. How many times greater is the population of Michigan than the population of South Dakota?
Express your answer as a whole number.
81
x2=81
9 and -9
The Mercedes Benz Stadium can hold up to 7.1 x 104 people. Truist Park can hold about 4.1 x 104. How many more people can the Mercedes Benz Stadium hold than Truist Park?
Express your answer in standard notation.
3000
Select the THREE correct statements.
A. 8/9 is an rational number because the decimal equivalent repeats.
B. 4/16 is an irrational number because the decimal equivalent terminates.
C. -4pi is an irrational number because the decimal equivalent does not terminate or repeat.
D. The cube root of 216 is a rational number because the cube root of 216 is an integer.
E. The square root of 364 is an irrational number because the square root of 364 is an integer.
ACD
Axel has a square piece of tissue paper that has an area close to 300 centimeters squared. What is a good approximation for the length of one side of his paper?
17 centimeters
A TV has dimensions of 44 and 48. Kobe says the area of the TV is 412 because you need to add the exponents. Andre says the area of the TV is 432 because you need to multiply the exponents. Explain who is correct and why.
Kobe because area is length times width, which means he needs to use the product rule and add the exponents.
x3=64
4
Simplify the expression. Express your answer in scientific notation.
(9.3 x 105) + (8.2 x 104)
1.012 x 106
Determine if 0.212112111211112111112... is rational or irrational and give a reason for your answer.
It is irrational because it is a decimal that does not repeat or terminate.
Maci wanted to build a fence around her house. The area of her house is 2,400 feet squared. About how long is her fence on one side of the house?
49 feet
What value of n will make the equation true?
(2n*23)5=235
4
x3=-216
-6
The diameter of Uranus is 14 x 106 kilometers and the diameter of Mars is 7 x 103. Approximately how many times the diameter of Uranus is the diameter of Mars? Write in scientific notation and round to the nearest tenth.
2 x 103