Main Idea and New Vocabulary

Key Concept: Square Root

Example 1: Find Square Roots

Example 2: Find Square Roots

Example 3: Find Square Roots

Example 4: Find Square Roots

Example 5: Use Square Roots to Solve an Equation

Example 6: Real-World Example

• Find square roots of perfect squares.

• perfect square

• square root

• radical sign

Find Square Roots

Find .

Answer: 9

Find the positive square root of 81; 92 = 81.

A. 5

B. 10

C. –10 or 10

D. no real square root

Find .

Find Square Roots

Find .

Find both square roots of 1.44; 1.22 = 1.44.

Answer: 1.2

A. 6

B. 0.6

C. 0.6

D. 0.06

Find .

Find Square Roots

Find .

Answer:

Find the negative square root of

Find .

A.

B.

C.

D. no real square root

Find Square Roots

Find .

Answer: There is no real square root because no number times itself is equal to –49.

A. –11

B. 11 or –11

C. –1.1

D. no real square root

Find .

Use Square Roots to Solve an Equation

ALGEBRA Solve x2 = 225.

x2 = 225 Write the equation.

x = Definition of square root

Answer: The equation has two solutions,

15 and –15.

x = 15 and –15 Check 15 • 15 = 225 and (–15)(–15) = 225

A. 20

B. 20 and –20

C. 40 and –40

D. no real square root

ALGEBRA Solve n2 = 400.

PUZZLE A square puzzle has an area of 35,721 square millimeters. What is the length of a side of the square?

s2 = 35,721 Write the equation.

35,721 = 3 • 3 • 3 • 3 • 3 • 3 • 7 • 7 Find the prime factors.

= (3 • 3 • 3 • 7)(3 • 3 • 3 • 7) Regroup into two equal factors.

Definition of square root

To find , find two equal factors of 35,721.

Answer: Since distance cannot be negative, the

length of each side is 189 millimeters.

So, s = 3 • 3 • 3 • 7 or 189.

A. 57 ft

B. 114 ft

C. 228 ft

D. 6,498 ft

MAZES A square corn maze has an area of 12,996 square feet. What is the length of a side of the square?