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4.6/4.7 Squares and Square Roots/Estimating Square Roots, p192/96
Warm Up Simplify.
1. 52 =
2. 82 =
3. 122 =
4. 152 =
5.
202 =
6. Find the area
1.5
NS2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square
integer.
LO: I will evaluate squares & square roots using
exponents with 2 degrees of power.
So √64 = 8 represents the principal square root;
and -√64 = -8 represents the negative square root.
THEREFORE: You can write √64 = ±8, which is read as “The square
root of sixty-four is plus or minus eight.”
perfect
perfect
A PERFECT
SQUARE is a
number that has
square roots that
are integers.
 √perfect is a
RATIONAL
NUMBER.
Square Roots
that are between
two integers are
estimates.
 √between is
an IRRATIONAL
NUMBERS.
between
ALWAYS use the PRINCIPAL (positive integer) square root for DISTANCE.
1. A square shaped kitchen table has an area of 16 square feet. Will it
fit through a van door that has a 5 foot wide opening?
√16 =
The table is __ feet wide, which is less than __ feet. ___ the table _____
fit through the van door.
2. A square window has an area of 1.69 square feet. How wide is the
window?
So √1.69 = _____; therefore the window is _____ feet
1.69 = ___2
wide .
3. Ms. Estefan wants to put a fence around 3 sides of a square garden
that has an area of 225 ft2. How much fencing does she need?
4. The floor of a square room has an area of 256
ft². What is the perimeter of the room?
5. A chessboard contains 32 black and 32 white squares. How many squares are along
each side of the game board?
√
< √55 < √
7<
<8
√55 is between two perfect squares, therefore the √55 is _________________.
√
< √80 < √
<
<
√80 is between two perfect squares, therefore the √80 is _________________.
A Coast Guard boat searching for a lost sailboat covers a square area of 185
mi2. What is the approximate length of each side of the square area? Round
your answer to the nearest mile.
√___ < √185 < √___
Each side of the search area is about ____ miles long.
The √185 is ____________ two perfect squares, therefore the
√185 is ___________________.
HW- Day 1- 4.6/7 Use a piece of paper to evaluate the problems on this slide.
4.6/4.7 Day 2 Squares and Square Roots of Monomials,
p192
LO: I will evaluate the square roots of monomials
using exponents with 2 degrees of power.
When evaluating monomial square roots:
Use raising a power to a power- Start with ? times 2 = the exponent
144c8
=√(12c
)2
= 12c
THINK: what number times 2 = the exponent?
(c-)²
Write the monomial as a square.
A variable raised to an ODD power uses the ABSOLUTE VALUE SYMBOL..
z6 = √(z )2
= ⃒z ⃒
THINK: what number times 2 = the exponent?
(z-)²
Write the monomial as a square.
Write the monomial as a square.
A. √121r2 =
THINK: (r-)²
D. √100n4 =
B. √p8 =
THINK: (p-)²
E. √16y¹⁴
C. √81m4 =
THINK: (m-)²
F. √m²g6 =
Remember:
A variable raised to an even power is always positive.
A variable raised to an ODD power uses the ABSOLUTE VALUE SYMBOL.
Find the two square roots of each number.
G. √144 =
H. √2500 =
THINK: what number times 2 = the exponent? (z-)²
Write the monomial as a square.
√x² =
√x⁴ =
√x⁶ =
√x⁸ =
√x¹⁰ =
√x¹² =
1. Look for a pattern. Make a conjecture about when you do not need to use an absolute
value in your answer.
Think and Discuss
2. Describe what is meant by a perfect square. Give and example.
3. Explain how many square roots a positive number can have. How are these square
roots different?
***Day 2 4.6 RM p31 & 4.7 SRp199#50-59 even