Squares & Square Roots
The area of a square is 49 square units. What is its side length?
What is 7?
Is 3/5 a rational or irrational number?
What is rational?
State the Pythagorean Theorem using the variables a, b, and c.
What is a² + b² = c²?
In a right triangle, which side is opposite the right angle?
What is the hypotenuse?
What is the cube root of 8? (∛8 = x)?
What is 2?
What mathematical relationship helps find distances between two points on a coordinate plane?
What is the Pythagorean Theorem?
A tilted square has an area of 73 square units. Express its side length as a square root.
What is √73?
Is √2 a rational or irrational number?
What is irrational?
In a right triangle with legs 3 and 4, what is the length of the hypotenuse?
What is 5?
In a right triangle, which two sides make the right angle?
What are the legs?
Solve: x³ = 27
What is 3?
A pencil is 17 cm long and fits diagonally in a cylindrical cup 15 cm tall. What is the diameter of the cup?
What is 8 cm?
Estimate the side length of a square with area 72 square units. (Choose from the following: 8 units, 8.5 units, 9 units)
What is 8.5 units?
Convert the repeating decimal 0.2̄5̄ (where both digits repeat) to a fraction in lowest terms.
What is 23/90?
A right triangle has a hypotenuse of 4 and one leg of 3. What is the length of the other leg?
What is √7?
Which set gives a right triangle?
Option A: (√3, √4, √5) or Option B: (3, √7, 4)
What is Option B: (3, √7, 4)?
Select all solutions to x³ = 27:
(A) 3 (B) ∛27 (C) 9 (D) 27³
What are A and B?
In a word problem involving a ladder leaning against a wall, what are you typically asked to find?
What is the diagonal (or height or distance)?
A square has a side length of 11 units. Using the formula, what is its area?
What is 121 square units?
Write an algebraic argument to show that 10/7 cannot equal √2.
What is that (10/7)² ≠ 2, so 10/7 ≠ √2?
Which set forms a right triangle: (3, √7, 4) or (5, 10, 11)?
What is (3, √7, 4)?
Does a triangle with side lengths 4, 5, and 9 satisfy the Pythagorean Theorem?
What is No?
Is ∛25 between 2 and 3, or between 1 and 2? Explain your reasoning.
What is between 2 and 3? Because 2³ = 8 and 3³ = 27, and 25 is between them.
Using a cup with diameter 8 cm and height 15 cm, how much water can it hold? (Use V = πr²h)
What is 240π cm³ (or approximately 754 cm³)?
If (√144)² equals the area of a square, what is the area?
What is 144 square units?
Is π a rational or irrational number? Explain how you know.
What is irrational? It cannot be written as a fraction.
Find the exact length of the segment joining points (−5, 4) and (6, −3) on a coordinate plane.
What is √170 units?
Is a triangle with side lengths √9, √16, and √25 a right triangle? Explain why or why not.
What is Yes, because 9 + 16 = 25?
If a cube has a volume of 8 cubic units, what is the length of one edge?
What is 2 units?
Write a general formula for finding the distance between any two points (x₁, y₁) and (x₂, y₂) on a coordinate plane.
What is √[(x₂ − x₁)² + (y₂ − y₁)²]?