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Gnoma [55]
3 years ago
15

Can anyone help me solve this

Mathematics
2 answers:
iren [92.7K]3 years ago
8 0

\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}}}}}

GREYUIT [131]3 years ago
8 0

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}

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