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If you responded "True" to Question 3, explain why using words and/or math to explain why the radical expressions can be combined.If you responded "False" to Question 3, explain why using words and/or math to explain why the radical expressions cannot be combined.

If you responded "True" to Question 3, explain why using words and/or math-example-1

2 Answers

3 votes

Answer:

Combine Like Terms ... Explain why you should simplify each radical in a radical expression before ... State whether each sentence is true or false.

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Step-by-step explanation:

User Nick Anderegg
by
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2 votes
Answer:

False

Because the radicals are not like terms

Step-by-step explanation:

The radical expressions are:


\sqrt[]{2}\text{ and }\sqrt[]{12}

Note that only like radicals can be combined using addition or subtraction

For examples:


a\sqrt[]{b}+c\sqrt[]{b}=(a+c)\sqrt[]{b}

The addition is possible because the same term (b) is inside the root

operator


\begin{gathered} \text{For }\sqrt[]{2}\text{ and }\sqrt[]{12} \\ \sqrt[]{12}=\sqrt[]{4*3}=2\sqrt[]{3} \\ \sqrt[]{2}\pm\sqrt[]{12}=\sqrt[]{2}\pm2\sqrt[]{3} \end{gathered}

Since the numbers under the roots are not the same, the radicals are not line radicals, hence cannot be combined by addition or subtraction

User Cfreak
by
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