Answered

3.3 Sam tried to simplify the algebraic expressions below. He obtained the answers below.

Look at the solutions he got and then:
- Indicate if you agree with the solution OR
- Redo the calculations indicating the correct steps.

a) [tex]\sqrt{16 a^{16} + 9 a^{16}}[/tex]
[tex]\[
\begin{array}{l}
= 4 a^4 + 3 a^4 \\
= 7 a^4
\end{array}
\][/tex]

---

Note: Please verify if the simplification and calculations provided by Sam are correct. If not, provide the correct steps and solution.



Answer :

GinnyAnswer
Let's analyze and simplify the given algebraic expression step-by-step:

The original expression is:
[tex]\[ \sqrt{16a^{16} + 9a^{16}} \][/tex]

First, we combine like terms inside the square root:
[tex]\[ 16a^{16} + 9a^{16} = (16 + 9)a^{16} = 25a^{16} \][/tex]

Next, we can simplify the square root of the combined term:
[tex]\[ \sqrt{25a^{16}} \][/tex]

We know that the square root of a product is the product of the square roots:
[tex]\[ \sqrt{25a^{16}} = \sqrt{25} \times \sqrt{a^{16}} \][/tex]

Now, we find the square roots of each of the components:
[tex]\[ \sqrt{25} = 5 \][/tex]
[tex]\[ \sqrt{a^{16}} = a^8 \][/tex]

(Recall that [tex]\(\sqrt{a^{16}} = a^{16/2} = a^8\)[/tex])

Putting it all together, we get:
[tex]\[ \sqrt{25a^{16}} = 5a^8 \][/tex]

Therefore, Sam's given answer of [tex]\( 7a^4 \)[/tex] is incorrect. The correct simplified form of the expression is:
[tex]\[ 5a^8 \][/tex]

Other Questions