Certainly! Let’s solve the given expression step-by-step.
We start with the expression inside the square root:
[tex]\[ \sqrt{9a^4 + 16a^4} \][/tex]
1. Combine like terms: Notice that both terms inside the square root have [tex]\(a^4\)[/tex] in them. We can factor out [tex]\(a^4\)[/tex] to combine them:
[tex]\[ 9a^4 + 16a^4 = (9 + 16)a^4 \][/tex]
So,
[tex]\[ 9a^4 + 16a^4 = 25a^4 \][/tex]
2. Simplify the expression: Now we substitute [tex]\(25a^4\)[/tex] back into the square root:
[tex]\[ \sqrt{25a^4} \][/tex]
3. Take the square root:
The square root of a product is the product of the square roots:
[tex]\[ \sqrt{25a^4} = \sqrt{25} \cdot \sqrt{a^4} \][/tex]
Knowing that:
[tex]\[ \sqrt{25} = 5 \][/tex]
[tex]\[ \sqrt{a^4} = a^2 \][/tex]
Hence:
[tex]\[ \sqrt{25a^4} = 5a^2 \][/tex]
Thus, the final simplified answer is:
[tex]\[ 5a^2 \][/tex]
