6th Grade Math Textbook, Fundamentals

(Marvins-Underground-K-12) #1
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.


  1.  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
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