Number and Logic: Reasoning and Radicals

Inductive and deductive reasoning, counterexamples, operations on radicals and solving radical equations.

17 questions, free, marked as you go with a worked explanation on every one.

What this covers

Express √72 as a mixed radical in simplest form.
Solve for x: √(2x + 3) = 5.
Simplify √18 + √50 to the form k√2. What is the value of k?
Which of these is the correct first step in rationalizing the denominator of 5 / √3?
Solve for x: ∛(x - 1) = 3.
A student conjectures that for every whole number n, the value of n² + n + 11 is prime. Which one of these values of n disproves the conjecture?
Which of the following are true about solving radical equations?
A square patio has an area of 200 m². A landscaper wants to know its side length so she can order edging. Express the side length as a mixed radical k√2 and give the value of k.
Simplify: √50
Evaluate √144.
A student claims: 'If a number is divisible by 4, it is always divisible by 8.' Which value disproves this claim?
Simplify: √18 + √8
In a class of 30 students, 18 play soccer and 12 play basketball. 5 students play both sports. How many students play neither sport?
The set of elements that belong to both set A and set B is called their:
The set of all elements that belong to A or B or both is called their:
Set A has 15 elements and set B has 9 elements. If A and B have 4 elements in common, how many elements are in the union of A and B?
A survey finds that every student who likes math also likes science, but not every student who likes science likes math. What is the correct relationship between the two sets?