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Which expression is equivalent to [tex]13 \sqrt{22 b} - 10 \sqrt{22 b}[/tex], if [tex]b \ \textgreater \ 0[/tex]?

A. [tex]23 \sqrt{22 b}[/tex]
B. [tex]130 \sqrt{22 b}[/tex]
C. [tex]3 \sqrt{b^2}[/tex]
D. [tex]3 \sqrt{22 b}[/tex]

Sagot :

GinnyAnswer
To simplify the expression [tex]\( 13 \sqrt{22b} - 10 \sqrt{22b} \)[/tex], we need to combine like terms.

In this case, both terms share the common factor [tex]\(\sqrt{22b}\)[/tex]. Here are the steps to simplify:

1. Identify the common factor in both terms:
[tex]\[ 13 \sqrt{22b} - 10 \sqrt{22b} \][/tex]

2. Factor out the common factor [tex]\(\sqrt{22b}\)[/tex]:
[tex]\[ (13 - 10) \sqrt{22b} \][/tex]

3. Perform the subtraction:
[tex]\[ 3 \sqrt{22b} \][/tex]

So, the simplified expression is:
[tex]\[ 3 \sqrt{22b} \][/tex]

Therefore, the expression [tex]\(13 \sqrt{22b} - 10 \sqrt{22b}\)[/tex] simplifies to [tex]\(3 \sqrt{22b}\)[/tex].

Hence, the correct answer is:
D. [tex]\(3 \sqrt{22 b}\)[/tex]
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