Right Triangles and Cube Roots

This video tutorial covers the Pythagorean Theorem and irrational numbers, focusing on geometric and symbolic representations of square and cube roots. It introduces essential vocabulary and explains the relationship between side lengths and areas of squares. The Pythagorean Theorem is detailed, showing how it applies to right triangles and can be used to solve problems. The concept of cube roots is also introduced, explaining how they relate to the volume of cubes.

Which of the following is NOT an essential vocabulary word introduced in the unit?

• Trapezoid

• Cube root

• Hypotenuse

• Rational number

What is the side length of a square with an area of 10 square units?

• 10 units

• Square root of 10

• 4 units

• 3 units

If a square has an area of 16 square units, what is its side length?

• 16 units

• 4 units

• 8 units

• 2 units

Which statement is true about the Pythagorean theorem?

• It applies to all triangles.

• It only applies to isosceles triangles.

• It describes the relationship between the sides of a right triangle.

• It is used to calculate the area of a circle.

In a right triangle, what is the side opposite the right angle called?

• Hypotenuse

• Leg

• Base

• Altitude

If the legs of a right triangle are 24 and 7, what is the length of the hypotenuse?

• 24 units

• 17 units

• 31 units

• 25 units

What is the cube root of a cube with a volume of 64 cubic units?

• 16

• 8

• 4

• 2

Which of the following is true about cube roots?

• They are always integers.

• They are the same as square roots.

• They can be plotted on a number line.

• They are only used for perfect cubes.

What is the edge length of a cube with a volume of 27 cubic units?

• 6 units

• 27 units

• 9 units

• 3 units

Which of the following is NOT a property of cube roots?

• They can be integers.

• They are always positive.

• They can be plotted on a number line.

• They represent the edge length of a cube.