5.3
Solving Quadratic Equations by
Finding Square Roots
Review Radicals
•Simplifying
•Multiplying
•Dividing/Rationalizing
RADICAL
3
RADICAL
SIGN
RADICAND
Reducing Radicals
18
96
6 • 15
3 12 • 6
6• 8
Reducing Radicals
7
4
7
2
25
3
3
2
Solving with Square Roots
1. Get x2 by itself
2. Take the square root of BOTH
sides of the equals sign
3. Simplify
Examples. Solve the equation. Simplify all radicals.
2
1. x = 4
x
2
= 4
x = ±2
2
2. n = 5
2
n = 5
n=± 5
Let’s look at
some examples
2
where x is NOT
by itself.
We must solve to get x2 by itself 1st!
Solve
2
2x
+ 1 = 17
We must solve to get x2 by itself 1st!
Solve
2
4x
– 6 = 42
We must solve to get x2 by itself 1st!
SOLVE
2
3 − 5 x = −9
We must solve to get x2 by itself 1st!
2
SOLVE
3 ( x − 2 ) = 21
We must solve to get x2 by itself 1st!
SOLVE
1
2
( x − 4) = 6
5
We must solve to get x2 by itself 1st!
SOLVE
1
2
(x + 5) = 7
3