Learn on PengiPengi Math (Grade 8)Chapter 2: Exponents, Radicals, and Scientific Notation

Lesson 4: Applications and Approximations of Square Roots

In this Grade 8 lesson from Pengi Math Chapter 2, students apply square roots and cube roots to solve geometric problems, such as finding missing side lengths of squares and edge lengths of cubes given their volume. Students also learn to identify perfect squares and approximate square roots of non-perfect squares using nearby perfect squares. These skills are then used to estimate and interpret results in real-world situations.

Section 1

Area of a Square

Property

Area, $A = s^2$
Length of a side, $s = \sqrt{A}$
We can use the formula $s = \sqrt{A}$ to find the length of a side of a square for a given area.

Examples

A square garden has an area of 150 square feet. The length of each side is $s = \sqrt{150} \approx 12.2$ feet.

A square photo has an area of 81 square inches. The length of each side is $s = \sqrt{81} = 9$ inches.

Section 2

Volume and surface area of a cube

Property

A cube is a rectangular solid whose length, width, and height are equal. For any cube with sides of length $s$ :

Volume: $V = s^3$

Surface Area: $S = 6s^2$

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Area of a Square

Property

Area, $A = s^2$
Length of a side, $s = \sqrt{A}$
We can use the formula $s = \sqrt{A}$ to find the length of a side of a square for a given area.

Examples

A square garden has an area of 150 square feet. The length of each side is $s = \sqrt{150} \approx 12.2$ feet.

A square photo has an area of 81 square inches. The length of each side is $s = \sqrt{81} = 9$ inches.

Section 2

Volume and surface area of a cube

Property

A cube is a rectangular solid whose length, width, and height are equal. For any cube with sides of length $s$ :

Volume: $V = s^3$

Surface Area: $S = 6s^2$