6th Grade Math Textbook, Fundamentals

Lesson 10-3 for exercise sets. &KDSWHU 

3UDFWLFH   $FWLYLWLHV

To use a calculator to find , press the following keys:

2 8 0 9

So 53.

Find both square roots of each number.

1. 169 2. 196 3.10,000 4.20,736

Simplify each expression.

5.  15 6. 7.  1 8. 

9.Discuss and Write Use graph paper and try to construct a square

with whole number side lengths and an area of 12 square units.

Why is it not possible to construct this square?

1322  12 64  9 1 196 25  16

2809

2809

53

Find the square root of 324.

n

n^2  324

2 • 2 • 3 • 3 • 3 • 3

(2 • 3 • 3)(2 • 3 • 3)

(2 • 3 • 3)^2

(2 • 9)^2

 182

So 18.

324

324

1 Simplify the expression.

 Evaluate powers.

 Add or subtract under radical sign.

 7 Simplify radical.

49

64  25 10

851022 ()

2 851022 ()

Remember:

The prime factorization of a

number shows the number

as the product of prime factors.

Simplify the expression 3.

 3 Add under radical sign.

 3 Find the square root.

 25  3 Simplify.

 28

400  225

625

(^3400)  225

You can use prime factorization to find the square root

of a perfect square. Find the square root of 225.

x Square both sides. ( )^2  225

x^2  225

3 • 3 • 5 • 5 Find the prime factorization of 225.

(3 • 5)(3 • 5) Rewrite as a product of two identical factors.

(15)(15) Simplify.

 152

So x3 • 5 15, and 15.

You can use what you know about perfect squares to simplify radical expressions.

225 225

225