Download Section 10.4

Mr. Borosky
Section 10.4
Algebra 1
10.4 Use Square Roots to Solve Quadratic Equations p. 652-658
Objective: 1. You will solve quadratic equations by finding square
roots.
To solve a quadratic equation of the form ax2 + c = 0 first isolate x2 on
one side to obtain x2 = d, then take the square root to solve.
Key Concept Box Solving
 If d > 0 then x2 =
 If d = 0 then x2 =
 If d < 0 then x2 =
x2 = d by taking Square Roots p. 652
d has 2 solutions:
x = ± d
d has 1 solution:
x = 0
d has no real solution
Square Root Of A Number – If x2 = b then “x” is a square root of “b”.
number that when multiplied by itself equals a given number. Square
roots are written with a Radical Sign (  ).
Examples: 32
= 9 so 3 is a square root of 9
Also
(-3)2 = 9 so –3 is a square root of 9
A
All Positive Numbers have 2 square roots.
1. Positive Square Root – Principal Square Root.
2. Negative Square Root
_
Radical – an expression denoted by √b
Radical Symbol – the root sign denoted by √
Radicand – the number or expression inside a radical symbol.
1. Positive Numbers have 2 square roots.
2. Zero ( 0 ) has 1 square root.
3. Negative Numbers have NO Real Square Roots.
every real number is Positive or Zero)
(because the square of
Simplest Form of a Radical Expression – an expression that has NO
Perfect Square factors other than 1 in the Radicand, NO Fractions in the
Radicand, and NO Radicals in the Denominator of a Fraction.
Summary: Simplest Form of a Radical Expression
1. No Perfect Square Factors other than 1 are in the Radicand.
Example: 8 = 4*2 = 22
2. No Fractions are in the Radicand
Example: 5/16
= 5 _
=
5
16
4
3. No Radicals are in the Denominator
Example: 1_
=
1 * 7
=
7
7
7 * 7
7
Product Property of Radicals – states the following
ab = a * b where a  0 and b  0
10.4 Use Square Roots to Solve Quadratic Equations p. 652-658
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Mr. Borosky
Section 10.4
Algebra 1
Quotient Property of Radicals – states the following
a/b
=
a
where a  0 and b  0
b
Rationalizing the Denominator – process of eliminating a Radical from a
Denominator by multiplying the Radical Expression by an appropriate
value of 1 (meaning you multiply the top and bottom of the fraction by
the same Radical).
10.4 Use Square Roots to Solve Quadratic Equations p. 652-658
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