Algebra 1 Common Core Student Edition, Grade 8-9

Go t I t? 3. What is the simplified form of each expression in parts (a)-(c)?

a. 3V6*Vl8 b. V2a • c. 7 Vox • 3 V20jc5

d. Reasoning In Problem 3, can you simplify the given product by first

simplifying V l4 f2? Explain.

Lhink
H o w is th is lik e
problems you have
done before?
The w id th a nd h e ig h t
o f th e do o r are tw o
legs o f a rig h t tria n g le.
This is like fin d in g th e
hypotenuse o f a rig h t
triangle using the
Pythagorean Theorem.

Writ ing a Radical Expression

Art A rectangular door in a museum is three times as

tall as it is wide. What is a simplified expression for the

maximum length of a painting that fits through the door?

Unow........................

The d o o r is w units w id e and

3w units high.

tan

Use th e P ythagorean Theorem.

The diagonal length d of

the doorway

d2 = w2 + (3 w)2 Pythagorean Theorem

d2 — w2 + 9 w2 Simplify (3w)2.

d2 = 10w2 Combine like terms.

d = VlOw/2 Find the principal square root o f each side.

d = Vur2 • VlO Multiplication Property of Square Roots

d = wV 10 Simplify V w 2.

An expression for the maximum length of the painting is w VTo, or about 3.16uc

& Got It? 4. A door's height is four times its width w. What is the maximum length of a

painting that fits through the door?

You can simplify some radical expressions using the following property.

Pr o p er t y Division Propert y of Square Roots

Algebra Example

For a s 0 and b > 0,. v fa \fab~Vb' V /36_ V36_6 49 V49 7

V J

When a radicand has a denominator that is a perfect square, it is easier to apply

the Division Property of Square Roots first and then simplify the numerator and

denominator of the result. When the denominator of a radicand is not a perfect square,

it may be easier to simplify the fraction first.

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Lesso n 10- 2 Si m p l i f y i n g Rad i cal s 621