Irrational numbers - practice problems

Irrational numbers are those that cannot be written in the form of a fraction, i.e. a rational number. They lie on the number line, but are not rational numbers. Typically, they are numbers with a non-periodic infinite decimal expansion. For example, Ludolf's number π=3.1415926..., Euler's number e = 2.71.... ; further roots, e.g. √2 = 1.41 ... √3 ... etc.

Direction: Solve each problem carefully and show your solution in each item.

Number of problems found: 11

Fraction or irrational
If you double 1/4 of a certain fraction and multiply it by that fraction, the answer is 1. What is the fraction?
Numeric question
Is it possible a negative, irrational number?
Roots
Calculate the square root of these numbers:
Expression 6
Evaluate expression: -6-2(4-8)-9
Expression 4333
Evaluate the expression 9-4x for x = 0, -2.3 / 4, 2.4, 5
Sandy
Sandy, John, and Marg baked pies for the Bake Sale. Sandy cut his pies into 6ths, John cut him into 8ths, and Marg cut hers into quarters. Sandy sold 11/6, John sold 1 3/8 pies, and Marg sold 9/4 pies. Who sold the most pies? Who sold the fewest?
A clerk
A clerk is paid 45.25 pesos per hour for 40 hours a week. 1.50 times the rate for overtime and double the rate for a holiday. How much does the clerk get if he works overtime for 5 hours and 2 hours on holiday?

Original price p
If the original price of a table is p and the sales price of the table is p-0.3p, which other expressions represent the sale price of the table? Calculate also for p=100 USD
Number
Is number 2.8814789 irrational?
Transforming cuboid
A cuboid with dimensions 6 cm, 10, and 11 cm is converted into a cube with the same volume. What is its edge length?
Logs
The trunk diameter is 52 cm. Is it possible to inscribe a square prism with a side 27 cm?

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