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Lesson: 9.4a Addition and Subtraction with...
uestion 9 of 10 , Step 1 of 1
$7 / 10$
Correct
Simplify the expression by combining the radical terms using the indicated operation(s). Assume all variables are positive.
\[
9 a \sqrt{50 a b}+2 a \sqrt{2 a b}-3 a \sqrt{8 a b}
\]

Step 1 ：The question is asking to simplify the expression by combining the radical terms. The terms are all under the square root, which means we can combine them if they have the same radicand (the number or expression underneath the square root).

Step 2 ：First, we need to simplify each term under the square root. For example, \( \sqrt{50ab} \) can be simplified to \( 5\sqrt{2ab} \) because \( 50 = 25*2 \) and the square root of \( 25 \) is \( 5 \).

Step 3 ：Similarly, \( \sqrt{2ab} \) is already in its simplest form, and \( \sqrt{8ab} \) can be simplified to \( 2\sqrt{2ab} \) because \( 8 = 4*2 \) and the square root of \( 4 \) is \( 2 \).

Step 4 ：After simplifying the terms under the square root, we can combine the terms that have the same radicand.

Step 5 ：The simplified form of the expression \( 9 a \sqrt{50 a b}+2 a \sqrt{2 a b}-3 a \sqrt{8 a b} \) is \( 41\sqrt{2}a\sqrt{ab} \). This is the simplest form of the expression, and we can't simplify it further.

Step 6 ：Final Answer: The simplified form of the expression \( 9 a \sqrt{50 a b}+2 a \sqrt{2 a b}-3 a \sqrt{8 a b} \) is \( \boxed{41\sqrt{2}a\sqrt{ab}} \).