Common Radical Expressions

Common Radical Expressions

Radical Expressions are called common if their radicands, the terms under the radical sign, have the same value.

Common Radicals Not Common Radicals

and and

Common Radical Expressions

Question 1:

Mari and Justin’s math teacher put two radical expressions on the board,

and

Mari said the two expressions were common radical expressions but Justin disagreed. Who is correct? Explain why they are correct.

Adding and Subtracting Radical Expressions

Adding and Subtracting Radical Expressions

Radical expressions with common radicals can be added or subtracted.

Example:

Adding and Subtracting Radical Expressions

Question 2:

Add

Adding and Subtracting Radical Expressions

Adding and Subtracting Radical Expressions

Radical expressions without common radicals cannot be added or subtracted.

Example:

However, sometimes radical expressions without common radicals become common radicals when simplified.

Example:

Adding and Subtracting Radical Expressions

Question 3:

Subtract

Adding and Subtracting Radical Expressions

Question 4:

Agent J and Agent K ran into Zargar from planet Zultar. Zargar said that since and can be any number then,

Is Zargar correct? Explain why or why not.

Multiplying and Dividing Radical Expressions

Multiplying and Dividing Radical Expressions

Unlike adding and subtracting radical expressions, you do not need common radicals to multiply or divide radical expressions.

To multiply, you simply multiply the numbers outside the radical together and then multiply the numbers inside the radical.

Example:

Multiplying and Dividing Radical Expressions

Question 5:

Multiply,

Multiplying and Dividing Radical Expressions

Multiplying and Dividing Radical Expressions

Sometimes when you multiple two radical expressions perfect square factors are the result. For that reason, it is usually best when combining the numbers in the radical to leave them factored until the very end.

Example,

Multiplying and Dividing Radical Expressions

Question 6:

Carmen multiplied together with another radical and got a result whose radical was Lynn said that was impossible. Who is right? Show that you are right saying who is right.

Dividing Radical Expressions

Dividing Radical Expressions

Similar to multiplying radicals, to divide you simply divide the numbers outside the radical and then divide the numbers inside the radical.

Example:

Dividing Radical Expressions

If a radical remains in the denominator, you rationalize the denominator as follows,

Dividing Radical Expressions

Question 7:

When would you rationalize the denominator?