Download 49 35 55 99 3 125 32 = 216∙ = 16∙ 2 = 4 2 ba ab ∙ =

Algebra 1 Notes SOL A.3 Radicals
Mrs. Grieser
Name: _______________________________________ Date: _______________ Block: ________
Radical Review

A perfect square is ______________________________________________.

The first 12 perfect squares are:____________________________________________________.

A square root of a number is ______________________________________________________.

Find:

Estimating square roots: find the closest perfect square
36
49
x2
144
35
o Estimate to the nearest whole number:

4x 4
55
99
Other roots:
o A perfect cube is ______________________________________________.
o The first 10 perfect cubes are:___________________________________________________.
o A cube root of a number is _____________________________________________________.
3

Find:

y means the xth root of y. The
the radicand.

By default, take the square root. Example:
3
8
3
27
3
x
125
x3
3
8x 6
symbol is called a radical. The number inside is
42 4= 2
Simplifying Radicals
A radical expression is in simplest form if:

No perfect squares other than 1 are in the radicand

No fractions are in the radicand

No radicals appear in the denominator of a fraction
We use the Product Property of Radicals and Quotient Property of Radicals to simplify:
Quotient Property of Radicals
The square root of a quotient equals the
quotient of the square roots of the
a
a

numerator and denominator:
ab  a  b
b
b
 Write the radicand as the product of perfect squares, and then take the roots of those
perfect squares.
a) Simplify 32
b) Simplify 9x 3
Product Property of Radicals
The square root of a product equals
the product of the square roots of the
factors:
32 = 16 2 = 16 ∙ 2 = 4 2
9x 3 =
9  x2  x =
You try: Simplify the radical expressions…
a) Simplify
24
b) Simplify
25x2
9 ∙ x 2 ∙ x = 3x x
Algebra 1 Notes SOL A.3 Radicals
Mrs. Grieser Page 2
Examples for Quotient Property of Radicals:
a) Simplify
13
=
100
13
13
=
10
100
b) Simplify
1
=
y2
1
y2
=
1
y
Multiplying Radicals
We can use the product property of to multiply radicals.
Examples:
a)
6∙ 6
= 36
=6
3x ∙4 x
= 4 3x x
b)
(makes sense!)
= 4 3x
= 3 7x 2 y 2
2
= 3xy 7
= 4x 3
Note: When we solve
7xy2 ∙3 x
c)
x 2 , we always take the positive value of x.
Rationalizing Denominators

The process of eliminating a radical in a denominator is called rationalizing the
denominator.
Examples: Rationalize the denominator…
5
7
5
5 7
7
=
∙
=
7
7 7
a)
b)
=
4
2x
2 2x
4
4 2x
2x
∙
=
=
x
2x
2x 2x
You try: Simplify the radical expressions…
a)
20
d)
96x2
1
x
g)
j)
3
 27x3
b)
72
c)
e)
9x
16
f)
h)
2x 2
5
i)
16x4
l)
k)
3
32x5
4
3
8
3n2
3
64x6 y 9
8