6th Grade Math Textbook, Fundamentals

276 Chapter 10

10-3

10 yd

5 yd

 5  4

√ 25 √ 25

 3  2  15210 34

The symbol , the , stands

for the positive square root of a number:

6 and 12.

A positive square root is also called the

principal square root.

radical sign

36 144

Update your skills. See page 411 XI.

Squares and Square Roots

Objective To find the square root of a perfect square• To understand negative square roots

of perfect squares• To simplify expressions involving perfect squares and square roots• To use

a calculator to find square roots

An archaeologist uses a grid map to divide a dig site into
four square regions of the same size, one for each of his four
students to explore and dig. The dimensions of the dig site
are 10 yards by 10 yards. What are the area and dimensions
of each student’s square region?

To find the area of a square with side length s, multiply s

by itself. Multiplying a number by itself, or raising it to the

second power, is finding the.

Use the formula for the area of a square, As^2 ,

to find the area of the total dig site.

As^2 area formula for a square

(10 yd)^2 Substitute the side length for s.

(10 yd)(10 yd) Evaluate the exponent.

100 yd^2 Simplify

There are 4 students, so each student has a square region

that is 100 yd^2 ÷ 4, or 25 yd^2 (“25 square yd”) to dig.

The numbers 100 and 25 are examples of square numbers, or perfect squares.

are squares of the counting (or natural) numbers, 1, 2, 3, 4, 5, ....

So the perfect squares are 1, 4, 9, 16, 25, 36, 49, and so on.

The third row in the table below shows the first ten perfect squares.

A of a number is a number that equals

the original number when multiplied by itself. Every

positive number has both a positive square rootand

a negative square root.

The positive square root of 100 is 10 because

10 • 10  102 100. The of a number

nis the side length of a square with area n. So a square

with an area of 100 yd^2 has a side length of 10 yd. The

positive square root of 25 is 5 because 5 • 5  52 25.

The of a number is the opposite

of the number’s positive square root.

Since (5)(5) 25, 5 is the negative square root

of 25. In symbols, 5. The negative square root

cannot represent the side length of a square.

So each archaeology student has a 5 yd by 5 yd square region to explore and dig.

negative square root

positive square root

Perfect squares

 25

square root

Counting Number 12345678910

Square of the Number 12 22 32 42 52 62 72 82 92 102

Perfect Square 1 4 9 16 25 36 49 64 81 100

square of the number