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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
• 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.
baba
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When ADDING and SUBTRACTING Square
Roots…..it is very similar to ADDING
and SUBTACTING
LIKE TERMS.
5 4 9x x x
5 3 4 3 9 3
Just as you ADD the LIKE TERM of X….
You ADD the LIKE TERM of ….
3COEFFICIENTS
LIKE TERMS
Make sure all Square Roots are in Simplest
Form.
Check for LIKE TERMS
Simplify all Square Roots
Once you Combine Like Terms,
You place the new Coefficient in front of
The Square Root.
ONLY ADD or SUBTRACT
Terms that have the SAME Square ROOT!
Add/Subtract the COEFFICIENTS
Adding and Subtracting Square Roots Flow Chart
2 6 4 6
2 4 6
24 4 6
6 6
2 6 4 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.
The terms are like radicals.
a.
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!
18 2
5 5 2 5 4 5
6 2 5 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.
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