Transcript square roots

How would you compare and
order roots of perfect
squares/cubes on a number line?
To compare any numbers, you want everything in
the same form.
Place the root on the number line where it would
fall.
0 1 2 3 4 5 6 7 8 9 10
Practice
• Place the following roots on a number line:
√25, √144, √4, √81
0 1 2 3 4 5 6 7 8 9 10 11 12
You do not have to use a number line to
compare: Look at your number line and
come up with a shortcut for comparing.
How do you recognize when a
square root is irrational?
• When you break it down using a factor
tree and you have #s left over, it is
irrational. If you cannot find one whole
number that multiplies by itself, the root is
irrational.
• You need to memorize your perfect
squares.
• Irrational Numbers
• The number √11 is an example of an
irrational number. An irrational number
cannot be written as a quotient of two
integers, and the decimal form of an
irrational number neither terminates nor
repeats. If n is a positive integer which is
not a perfect square, then n is an irrational
number.
Practice
• √24
√66
√84
In what ways can you approximate
square and cube roots?
• Step 1: Find what two whole numbers the
root would fall between. Example: √18
4*4 = 16
5*5=25 so the square root of
18 is between 4 and 5.
• Step 2:Next decide which number is it
closer to.
• Step 3: Guess and check with decimals
• Your turn:
• √32
√95
√138
Using number lines
7.3
√56
7.4
7.5
Activator
• Which of these number is irrational?
√0.36
-√49
√24
√1.69
How would you demonstrate your
understanding of square roots by
simplifying expressions?
• To simplify addition and subtraction
problems you think of the radical (√) as a
grouping symbol: you do everything under
the √ first then find the root.
• Practice:
√63 + 1=
√14 - -5 =
Practice: WB pg 143
• To simplify multiplication and division
problems you can rewrite the problem.
(similar to the distributive property)
• √ab = √a x √b
or √a/b= √a ÷ √b
Practice:
• Rewrite each problem as a multiplication
problem
√36 =
√8 x √8=
√56=
2√3=
Practice:
• Rewrite each division problem:
√12/24 =
√18 ÷ √9=
√14/7=
√9 ÷ √27=
Challenge
• Is the square root of the sum of two
perfect squares always, sometimes, or
never irrational? Use examples to prove
your choice.
• Is the square root of the product of two
perfect square always, sometimes, or
never irrational? Use examples to prove
your choice.