Answer :
To simplify the expression [tex]\(\sqrt{9x} - \sqrt{4x} + 4\sqrt{x}\)[/tex], follow these steps:
1. Simplify Individual Square Roots:
- [tex]\(\sqrt{9x} = \sqrt{9} \times \sqrt{x}\)[/tex].
Since [tex]\(\sqrt{9} = 3\)[/tex], it becomes [tex]\(3\sqrt{x}\)[/tex].
- [tex]\(\sqrt{4x} = \sqrt{4} \times \sqrt{x}\)[/tex].
Since [tex]\(\sqrt{4} = 2\)[/tex], it becomes [tex]\(2\sqrt{x}\)[/tex].
2. Rewrite the Expression:
Substitute the simplified terms back into the expression:
[tex]\[
\sqrt{9x} - \sqrt{4x} + 4\sqrt{x} = 3\sqrt{x} - 2\sqrt{x} + 4\sqrt{x}
\][/tex]
3. Combine Like Terms:
All the terms have [tex]\(\sqrt{x}\)[/tex], so you can combine them by adding or subtracting the coefficients:
- Coefficient of [tex]\(3\sqrt{x}\)[/tex] is 3
- Coefficient of [tex]\(-2\sqrt{x}\)[/tex] is -2
- Coefficient of [tex]\(4\sqrt{x}\)[/tex] is 4
Add the coefficients: [tex]\(3 - 2 + 4 = 5\)[/tex].
The expression becomes:
[tex]\[
5\sqrt{x}
\][/tex]
So, the expression [tex]\(\sqrt{9x} - \sqrt{4x} + 4\sqrt{x}\)[/tex] simplifies to [tex]\(5\sqrt{x}\)[/tex].
1. Simplify Individual Square Roots:
- [tex]\(\sqrt{9x} = \sqrt{9} \times \sqrt{x}\)[/tex].
Since [tex]\(\sqrt{9} = 3\)[/tex], it becomes [tex]\(3\sqrt{x}\)[/tex].
- [tex]\(\sqrt{4x} = \sqrt{4} \times \sqrt{x}\)[/tex].
Since [tex]\(\sqrt{4} = 2\)[/tex], it becomes [tex]\(2\sqrt{x}\)[/tex].
2. Rewrite the Expression:
Substitute the simplified terms back into the expression:
[tex]\[
\sqrt{9x} - \sqrt{4x} + 4\sqrt{x} = 3\sqrt{x} - 2\sqrt{x} + 4\sqrt{x}
\][/tex]
3. Combine Like Terms:
All the terms have [tex]\(\sqrt{x}\)[/tex], so you can combine them by adding or subtracting the coefficients:
- Coefficient of [tex]\(3\sqrt{x}\)[/tex] is 3
- Coefficient of [tex]\(-2\sqrt{x}\)[/tex] is -2
- Coefficient of [tex]\(4\sqrt{x}\)[/tex] is 4
Add the coefficients: [tex]\(3 - 2 + 4 = 5\)[/tex].
The expression becomes:
[tex]\[
5\sqrt{x}
\][/tex]
So, the expression [tex]\(\sqrt{9x} - \sqrt{4x} + 4\sqrt{x}\)[/tex] simplifies to [tex]\(5\sqrt{x}\)[/tex].