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6-8 Accelerated 7 Unit 8

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IM K-5 Math
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IM® 6-8 Math v.360, an IM v.360 curriculum, is ©2024 by Illustrative Mathematics®, and licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).

IM 6-8 Math v.360, an IM v.360 curriculum, is a derivative of IM 6-8 Math.

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Adaptations and additions to create IM 6–8 Math v.360 Accelerated are ©2025 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY-NC 4.0).

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Unit 8

Glossary

Accelerated 7

cube root

The cube root of a number is the number whose cube is . It is also the edge length of a cube with a volume of . The cube root of is written as .

The cube root of 64 is written as . Its value is 4 because is 64.

is also the edge length of a cube that has a volume of 64.

used in:

hypotenuse

The hypotenuse is the side of a right triangle that is opposite the right angle. It is the longest side of a right triangle.

Here are some right triangles. Each hypotenuse is labeled.

Four right triangles of different sizes and orientations each with two legs and a hypotenuse opposite the right angle.

used in:

irrational number

An irrational number is a number that is not rational. It cannot be written as a positive fraction, a negative fraction, or zero.

Pi () and are examples of irrational numbers.

used in:

legs

The legs of a right triangle are the sides that make the right angle.

Here are some right triangles. Each leg is labeled.

Four right triangles of different sizes and orientations each with two legs and a hypotenuse opposite the right angle.

used in:

Pythagorean Theorem

The Pythagorean Theorem describes the relationship between the side lengths of right triangles.

The square of the hypotenuse is equal to the sum of the squares of the legs. This is written as .

This diagram shows the relationship.

a right triangle with squares built on each side

used in:

rational number

A rational number is a number that can be written as a positive fraction, a negative fraction, or zero. It can be written in the form where and are integers and is not equal to 0.

For example, 0.7 is a rational number because it can be written as .

Some examples of rational numbers:

used in:

repeating decimal

A repeating decimal has digits that keep going in the same pattern over and over. The repeating digits are marked with a line above them.

The decimal representation for is , which means 0.3333333 . . . .
The decimal representation for is , which means 1.136363636 . . . .

used in:

square root

The square root of a positive number is the positive number whose square is . It is also the side length of a square whose area is . The square root of is written as .

The square root of 16 is written as . Its value is 4 because is 16.

is also the side length of a square that has an area of 16.

used in: