Lesson 4.5 and 4.6--Squares and Square Roots
To learn to find square roots.
To learn to estimate square roots. Recall:
Taking the square root of a nonnegative number is the opposite of
squaring the number.
So, Every positive number has two square roots, one positive and one
negative.
Let's think about this. For , if we ask ourselves "What number can
be multiplied by itself to form a product of 9?" What would the answer
be?
Since ____ and ____ both work, we say
The
______.
indicates the nonnegative or ______________ ____________
____________. If we wanted the negative square root we would write
it as
.
EX: Find each square root.
a.
b.
EX: Find the two square roots
of each number
a.
4
b. 81
A ______________ ____________ is a number that has integers as its
square roots.
Square 1
Root
2
3
4
5 6 7 8 9 10
Perfect Square
1
Order of Operations with Square Roots
Everything under the square root symbol is treated as if it were in
parentheses.
EX: Simplify each expression.
a.
b.
c.
You can use the square roots of perfect squares to estimate the square
roots of other numbers.
EX: Each square root is between two consecutive integers. Name the
integers. Show your work or explain.
a.
b.
We can also use our calculators to find more exact values for square
roots. EX: Use a caluclator to find
. Round to the nearest tenth.
Application
Think about the relationship between the area of a square
and the length of one of its sides.
Area of a square =
5
Area of this square =
5
So, if you know the area of a square, you can easily find the
length of one side by taking the ___________ __________.
EX: A square window has an area of 169 square inches. How wide is
the window? Write and solve an equation to find the length of a
side.
HW: WS
2