Rational Numbers as Decimals
Let x=0.233...
x=7/30
Is 3√9 a rational or irrational number?
Irrational.
Does 1/6, -3, √7, -6/5, or 4.5 come first when the numbers are listed least to greatest? Explain.
-3, the most negative number
A cube has a volume of 512 cubic inches. What is the area?
64 in.2
Solve the equation v3=12.
3√12
Let x=7.033...
Write as a mixed number.
x=7 1/30
How can you tell whether a square root of a whole number is a rational or irrational number?
It has to be a perfect square to be rational.
What is the decimal approximation of √90 to the nearest tenth?
9.5
Would you classify the number 729 as a perfect square, a perfect cube, both, or neither?
Both
√729 = 27
3√729 = 9
Solve x2 = 256.
x = 16 and x = -16
Let x=0.005...
x=5/900
Deena says that 9.565565556... is a rational number because it has a repeating pattern. Do you agree? Why or why not?
No, the same pattern isn't repeating.
Approximate √18 to the nearest tenth and plot the number on a number line.
4.2
Should be between 4.2 and 4.3 on the number line.
Diego says that if you cube the number 4 and then take the cube root of the result, you end up with 8. Is Diego correct? Explain.
No, the cube root of 43 is still 4. You only get 8 if you take the square root.
There is an error in the work shown below. Explain the error and provide a correct solution.
x3 = 125
3√x3 = 3√125
x = 5 and x = -5
The work is correct, but x ≠ -5 because it is the cubed root of a positive number so all answers are positive.
Let x = 2.855...
Write as a mixed number.
x=2 77/90
Is 0.444 a rational or irrational number? If it's rational, is it repeating or terminating?
Rational; terminating
√50 < 7 8/9
A toy has various shaped objects that a child can push through matching holes. The area of the square hole is 8 square centimeters. The volume of a cube-shaped block is 64 cubic centimeters. Will the block fit in the square hole? Why or why not?
Yes; √8 < 4 and 43 = 64, so (√8)3 < 64
The Traverses are adding a new room to their house. The room will be a cube with a volume of 6,859 cubic feet. They are going to put in hardwood floors, which costs $10 per square foot. How much will the hardwood floors cost?
$3,610
Let x=0.14204545...
x=25/176
Is √25pi a rational or irrational number?
Irrational.
25 is a perfect square, but pi isn't.
The area of a square poster is 31 square inches. Find the length of one side of the poster to the nearest tenth of an inch.
5.6 inches
Which expression has the greatest value? What is that value?
a) √49 x 2
b) √48 - √16
c) √25 + √16
d) √25 x 3
d) √25 x 3 = 15
Yael has a square-shaped garage with 228 square feet of floor space. She plans to build an addition that will increase the floor space by 50%. What will be the length, to the nearest tenth, of one side of the new garage?
√228 + √228/2