A.3 - Simplifying & Operations with Radicals

A.3 - Simplifying & Operations with Radicals

By Ms. Bergan

Look for groups of...

2 if it is a √​

3 if it is a ∛​

Make a Factor Tree

​

Desmos Hints

If you have a multiple-choice question: ​Use Desmos to try and match the values. -- If you get 2 answers that match choose the one that is more simplified (smaller numbers under the radical)​.

Desmos Abreviations: sqrt = √​ and cbrt = ∛

Multiple Choice

SOL Question: What is $$\sqrt[]{18}$$  written in simplest radical form?

• $$2\ \sqrt[]{3}$$  

• $$3\ \sqrt[]{2}$$  

• $$3\ \sqrt[]{6}$$  

• $$6\ \sqrt[]{3}$$  

Multiple Choice

SOL Question: When n>0, which expression is equivalent to $$\sqrt[]{42n^9}$$  in simplest form?

• $$n^3\ \sqrt[]{42}$$  

• $$n^4\ \sqrt[]{42n}$$  

• $$6n^{3\ }\sqrt[]{7}$$  

• $$6n^4\ \sqrt[]{7n}$$  

Multiple Select

SOL Question: Identify each expression that is in simplest radical form.

• $$x\ \sqrt[]{50y}$$  

• $$64\ \sqrt[]{x}$$   

• $$7x^2y\ \sqrt[]{2xy}$$  

• $$\sqrt[]{12x^3y^4}$$  

Multiple Choice

SOL Question: What is the value of $$\sqrt[]{128}$$  in simplest radical form?

• $$8\ \sqrt[]{2}$$  

• $$64\ \sqrt[]{2}$$  

• $$4\ \sqrt[]{8}$$  

• $$16\ \sqrt[]{8}$$  

Multiple Choice

SOL Question: Which is equivalent to $$\sqrt[3]{48}$$   in simplest form?

• $$2\ \sqrt[3]{6}$$  

• $$6\ \sqrt[3]{2}$$  

• $$16$$  

• $$24$$  

Multiple Choice

SOL Question: A student claims that $$\sqrt[3]{80}$$  is in simplest radical form. Which statement is true?

• The claim is correct because 80 is not divisible by three.

• The claim is correct because 80 is not a perfect cube.

• The claim is incorrect because 80 has a factor of 4.

• The claim is incorrect because 80 has a factor of 8.

Adding/Subtracting Radicals

Multiple Choice

• A
• B
• C
• D

Multiple Choice

√8 - 6√2

• -4√2
• 2√2
• -6√6
• -6√10

Multiple Choice

√5 × √10

• 50
• 2√5
• 5√2
• 5√10

Multiple Choice

√3 × √15 =

• 3√5
• 5√3
• 2√7
• √17