Topic: 5.1 Working
Name: ____________________________________
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With Radicals
Class: PrePre-Calculus Mathematics 11
Date: ____________________________________
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Questions/Main Ideas:
Learning Intention:
Notes:
Demonstrate an understanding of and ability to problem solve
using radical expressions.
expressions.
Quick Review:
Focus On: Converting between mixed radicals and entire
radicals.
Comparing and ordering radical expressions.
Identifying restrictions on the values for a variable in
a radical expression.
Simplifying radical expressions using addition and
and
subtraction.
Main Ideas
Ideas:
Like Radicals: Radicals with the same radicand and index are
called like radicals. When adding and subtracting radicals, only
like radicals can be combined. You may need to convert radicals
to a different form(mixed or entire) before identifying like
radicals.
Examples:
Pairs of Like Radicals
4√6 789 : √6
;<
<
<
√4=; 789 √4=;
Pairs of Unlike Radicals
;√4 789 ;√<
>
4
√47 789 √47
Restrictions on Variables: If a radical represents a real number
and has an even index, the radicand must be nonnon-negative.
The radicand √> : = has an even index. So, 4 –x must be
greater than or equal to zero.
>:=DE
>:=F=DEF=
>D=
The radical √> : = is only defined as a real number if x is less
than or equal to four. You can check this by substituting values
for x that are greater than four, equal to four and less than four.
Teaching Examples:
Convert Mixed Radicals to Entire Radicals
Express each mixed radical in entire radical form. Identify the
values of the variable for which the radical represents a real
number.
a) 6√;
b) 7> √7
<
c) 4H√<H;
Radicals in Simplest Form: A radical is in simplest form if the
Hint: Make a list of all
perfect squares when
converting radicals to
simplest form.
following are true.
• The radicand does not contain a fraction or any factor
which may be removed.
• The denominator does not contain a radical.
For example, √JK is not in simplest form because 18 has a
square factor of 9, which can be removed. √JK is equivalent to
the simplified form<√;.
form
Teaching Examples:
Express Entire Radicals as Mixed Radicals
Convert each entire radical to a mixed radical in simplest form.
a) √;EE
>
b) √NO
c) P>KQ4
Compare and Order Radicals
Five bentwood boxes, each in the shape of a cube have the
following diagonal lengths, in centimeters.
J
>(J<);
K√<
J>
√;E;
JE√;
Order the diagonal lengths from least to greatest without using a
calculator.
Add and Subtract Radicals
Simplify radicals and combine like terms.
a) √4E F <√;
b) :√;6 F <√4 : √KE : ;√J;
c) √>N : >√ON, N D E
Something challenging Apply Addition of Radical Expressions
Consider the design show for a
Skateboard ramp. What is the
Exact distance across the base?
Next Step:
#1#1-4, 5a, c, 6a, c, 8a, c, 9a, c, 10a, c, 15, 20
40cm
30°
30cm
30°