Sure, let's simplify the algebraic expression [tex]\(\sqrt{4x^2 + 21x^2}\)[/tex].
1. Combine like terms inside the square root:
The expression inside the square root is [tex]\(4x^2 + 21x^2\)[/tex]. These are like terms as they both have [tex]\(x^2\)[/tex].
2. Add the coefficients of [tex]\(x^2\)[/tex]:
[tex]\[
4x^2 + 21x^2 = (4 + 21)x^2 = 25x^2
\][/tex]
3. Take the square root of the simplified term:
[tex]\[
\sqrt{25x^2}
\][/tex]
4. Simplify the square root:
[tex]\[
\sqrt{25x^2} = \sqrt{25} \cdot \sqrt{x^2}
\][/tex]
We know that [tex]\(\sqrt{25} = 5\)[/tex] and [tex]\(\sqrt{x^2} = x\)[/tex], assuming [tex]\(x \geq 0\)[/tex].
5. Combine the results:
[tex]\[
\sqrt{25x^2} = 5x
\][/tex]
Therefore, the simplified expression is [tex]\(5x\)[/tex].
