Unit 1 Relationships Between
Quantities and Expressions
Week 2
Lesson 2 – Add/Subtract Radicals
(restricted to square roots only)
Today’s Objective
• MGSE9-12.N.RN.2 Rewrite expressions involving
radicals (restricted to square roots only)
• MGSE9-12.N.RN.3 Explain why the sum or product of
rational numbers is rational; why the sum of a
rational number and an irrational number is
irrational; and why the product of a nonzero rational
number and an irrational number is irrational.
• Objective: Students will Add, Subtract and
Simplify radical expressions
Essential Questions
• If you add two radicals will you always get
another radical?
• If you add two irrationals numbers will you get
another irrational number?
• How do you simplify a radical expression?
Vocabulary
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Simplify
Like Terms
Radicals
Radicands
Simplest Form
Factors
Read, Write, Draw, Solve
There are a list of numbers below. Sort the
numbers in order from least to greatest and
explain your thought process.
Sums and Differences
Rules in the previous section allowed us to
split radicals that had a radicand which was a
product or a quotient.
We can NOT split sums or differences.
ab  a  b
a b  a  b
When ADDING and SUBTRACTING Square
Roots…..it is very similar to ADDING
and SUBTACTING
LIKE TERMS.
Just as you ADD the LIKE TERM of X….
5x  4 x  9 x
COEFFICIENTS
You ADD the LIKE TERM of
5 34 3 9 3
LIKE TERMS
3….
Adding and Subtracting Square Roots Flow Chart
Make sure all Square
Roots are in Simplest
Form.
24  4 6
Add/Subtract the
COEFFICIENTS
24  6
Simplify all
Square Roots
2 6 4 6
ONLY ADD or
SUBTRACT
Terms that have the
SAME Square ROOT!
Check for LIKE TERMS
2 6 4 6
Once you Combine
Like Terms,
You place the new
Coefficient in front of
The Square Root.
6 6
Adding and Subtracting Square-Root Expressions
Add or subtract.
A.
The terms are like radicals.
B.
The terms are unlike radicals. Do not
combine.
Try This!
Add or subtract.
a.
The terms are like radicals.
b.
The terms are like radicals.
Sometimes radicals do not appear to be like
until they are simplified, Simplify all radicals
in an expression before trying to identify like
radicals.
Simplify Before Adding or Subtracting
Simplify each expression.
Factor the radicands using perfect squares.
Product Property of Square Roots.
Simplify.
Combine like radicals.
Simplify Before Adding or Subtracting
Simplify each expression.
Factor the radicands using perfect squares.
Product Property of Square Roots.
Simplify.
The terms are unlike radicals. Do not
combine.
Try This!
Simplify each expression.
Factor the radicands using perfect squares.
Product Property of Square Roots.
Simplify.
Combine like radicals.
Try This!
Simplify each expression.
Factor the radicands using perfect squares.
Product Property of Square Roots.
Simplify.
The terms are unlike radicals. Do not combine.
Geometry Application
Find the perimeter of the
triangle. Give the answer as a
radical expression in simplest
form.
Write an expression for perimeter.
Factor 20 using a perfect square.
Product Property of Square Roots.
Simplify.
Combine like radicals.
You try these!
6 2 5 2 
5 5 2 5 4 5 
18  2 
Find the perimeter of a rectangle whose
length is
inches and whose width is
inches. Give your answer as a radical
expression in simplest form.
1. Draw it
2. How do you find the perimeter?
Write an expression for perimeter 2 (l + w).
Multiply each term by 2 .
Simplify.
Combine like radicals.
Exit Ticket
• Find the perimeter of the trapezoid.
Give the answer as a radical expression in
simplest form.