Select the correct answer.

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

A. [tex]$23 \sqrt{226}$[/tex]
B. [tex][tex]$130 \sqrt{22 b}$[/tex][/tex]
C. [tex]$3 \sqrt{b^2}$[/tex]
D. [tex]$3 \sqrt{22 b}$[/tex]



Answer :

To find the expression equivalent to [tex]\( 13 \sqrt{22 b} - 10 \sqrt{22 b} \)[/tex], we can follow these step-by-step instructions:

1. Identify the Common Term: Both terms in the expression [tex]\( 13 \sqrt{22 b} - 10 \sqrt{22 b} \)[/tex] share a common factor, which is [tex]\( \sqrt{22 b} \)[/tex].

2. Factor Out the Common Term: We can simplify the expression by factoring out the common term, [tex]\( \sqrt{22 b} \)[/tex]. This means we are effectively grouping the terms together:
[tex]\[ 13 \sqrt{22 b} - 10 \sqrt{22 b} = (13 - 10) \sqrt{22 b} \][/tex]

3. Perform the Arithmetic Inside the Parentheses: Subtract 10 from 13 inside the parentheses:
[tex]\[ (13 - 10) \sqrt{22 b} = 3 \sqrt{22 b} \][/tex]

4. Conclusion: After simplifying, we find that the equivalent expression is:
[tex]\[ 3 \sqrt{22 b} \][/tex]

In the provided options:
- Option A: [tex]\( 23 \sqrt{226} \)[/tex] does not match.
- Option B: [tex]\( 130 \sqrt{22 b} \)[/tex] does not match.
- Option C: [tex]\( 3 \sqrt{b^2} \)[/tex] does not match.
- Option D: [tex]\( 3 \sqrt{22 b} \)[/tex] is the correct match.

Thus, the correct answer is [tex]\( \boxed{D} \)[/tex].