Question

Can anyone help me solve this

Answer 1

$\longrightarrow{\green{ D. \:3 {a}^{4} \sqrt{2a} }}$ 

$\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}$

$\sqrt{18 {a}^{9} } \\ \\ ➝ \: \sqrt{2 \times 3 \times 3 \times {a}^{9} } \\ \\ ➝ \: \sqrt{2 \times ({3})^{2} \times {( {a}^{4}) }^{2} a } \\ \\ [∵( { {a}^{4} )}^{2} a = {a}^{4 \times 2 + 1} = {a}^{9}] \\ \\ ➝ \: 3 \times {a}^{4} \sqrt{2a} \\ \\ ➝ \: 3 {a}^{4} \sqrt{2a}$

$\pink{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}$

Answer 2

Answer:

The answer is $3a^{4}\sqrt{2a}$

Step-by-step explanation:

To simplify the radical, start by factoring 9 out of 18 for step 1. Next, for step 2, rewrite 9 as $3^{2}$. Then, factor out $a^{8}$ for step 3. For step 4, rewrite $a^{8}$ as $(a^{4})^{2}$. Then, for step 5, move the 2 in the radical. Rewrite $3^{2}(a^{4})^{2}$as $(3a^{4})^{2}$ for step 6. Then, add parentheses to the radical for step 7. Finally, for step 8 pull the terms out from under the radical, and the answer is $3a^{4}\sqrt{2a}$.  

Step 1: $\sqrt{9(2)a^{9} }$

Step 2: $\sqrt{3^{2}*2a^{9}$

Step 3:  $\sqrt{3^{2}*2(a^{8}a) }$

Step 4: $\sqrt{3^{2}*2((a^{4})^{2}) }$

Step 5: $\sqrt{3^{2}(a^{4})^{2}*2a }$

Step 6: $\sqrt{(3a^{4} )^{2}*2a }$

Step 7:  $\sqrt{(3a^{4})^{2}*(2a) }$

Step 8: $3a^{4}\sqrt{2a}$