Transcript square root

Do Now 4/19/10
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Copy HW in your planner.
 Text p. 655, #4-48 multiples of 4, #56 & 60
A= 36
A = 6²
A= 16
A = 4²
What is the area for each figure?
What are the dimensions for each
figure?
6
Write an equation for area of the
figure?
Can you think of an equation
for ONE side of the figure?
4
4
6
Objective
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SWBAT solve quadratic equations by
finding square roots
Remember This???
Section 2.7 “Find Square Roots and Compare Numbers”
If b² = a then
b is the square root of a.
The SQUARE ROOT of a number
is denoted by the symbol
,
which is called a radical.
9 3
radicand
Square Roots
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All positive real numbers have two square roots, a
positive and negative square root.
The symbol  is read as “plus or minus” and refers to
both the positive and negative square root.
Negative real numbers do not have real square roots.
So there is no solution.
9  3
 25 
no
solution
The square of an integer is called a perfect square.
10  100
2
(9) 2  81
Not PERFECT???
10  ?
The square root of a whole number that is NOT a
perfect square is an
IRRATIONAL NUMBER.
numbers that cannot be written as a
quotient (fraction, ratio) of two integers
and the decimal neither terminates nor
repeats.
To find the square root of a
number that is not a perfect square
estimate or use a calculator to find the
square root.
10  3.162276601...
Section 10.4 “Use Square Roots to Solve
Quadratic Equations”
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To use square roots to solve a quadratic equation of the
form ax² + bx + c = 0, first isolate x² on one side of the
equation to obtain x² = d.
Solving x² = d by Taking Square Roots
- If d > 0, then x² = d has two solutions:
x d
Examples
2x2  8
x  2
x2  4
- If d = 0, then x² = d has one solution:
x0
x 2  18  18
x0
x2  0
- If d < 0, then x² = d has no solution:
no solution
x 2  12  7
x 2  5
no
solution
Try It Out…
c 2  25  0
5a 2  12  8
c  25
5a  20
c   25
c  5
a  4
2
2
2
No solution
2 y  11  11
x  4  14
2y  0
x 2  10
y 0
x   10
x  3.16
2
2
2
y0
2
Take square roots of a fraction
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In cases where you need to take the
square root of a fraction whose numerator
and denominator are perfect squares, the
radical can be written as a fraction.
For example,
4
16
can be written as
.
5
25
Try It Out…
4c 2  9
9
c 
4
2
9
c
4
3
c
2
25b 2  18  2
25b 2  16
16
2
b 
25
16
b
25
4
b
5
Solve the quadratic equation. Round your
answer to the nearest hundredth.
6( x  4)  42
3(t  5)  24
( x  4) 2  7
(t  5) 2  8
2
( x  4)  7
2
x4   7
x  4  2.65
x  6.65; _ 1.35
2
(t  5)  8
2
t 5   8
t  5  2.83
t  7.83; _  2.17
Homework
Text p. 655, #4-48 multiples of 4,
#56 & 60