I NEED HELP RN PLEASEEEE ITS AN EMERGENCY!! Simplify. The square root of 24 multiplied by the square root of 12

Question

I NEED HELP RN PLEASEEEE ITS AN EMERGENCY!!

Simplify.

The square root of 24 multiplied by the square root of 12

Answer Choices:

A) 2sqroot 12
B) 6
C) 12sqroot 2
D) 288

I need the CORRECT ANSWER ASAP! (worth 10 points)

in progress 0
Lydia 2 weeks 2021-10-10T21:50:37+00:00 2 Answers 0

Answers ( )

    0
    2021-10-10T21:51:50+00:00

    Answer:

    The answer is C) 12\sqrt{2}.

    Step-by-step explanation:

    For a real number a,

    \sqrt{a} \cdot \sqrt{a} = a.

    In other words, multiplying a square root by itself gets rid of the square root.

    How does this rule apply here?

    24 = 2\times 12.

    Similarly,

    \sqrt{24} = \sqrt{2}\times \sqrt{12}.

    That is:

    \begin{aligned}\sqrt{24}\times \sqrt{12} &= (\sqrt{2}\times \sqrt{12}) \times \sqrt{12}\\&=\sqrt{2}\times (\sqrt{12}\times \sqrt{12}) && \begin{array}{l}\text{By the associative property}\\\text{of multiplication}\end{array}\\&=\sqrt{2} \times 12\\ &= 12\sqrt{2}\end{aligned}.

    0
    2021-10-10T21:51:58+00:00

    Answer:  The correct answer is:  [C]:

    ______________________________________________

                       →   12sqroot ” ;   or, write as:  ” 12√2 ” .

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    Step-by-step explanation:

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    √24 * √12 = ?

    Let us start by simplifying:  ” √24 ” ;

       24 = 4 * 6 ;

    So;  √24 = √4 *√6  ;

      √4 = 2 ;

    So:  ” √24  = √4 *√6  =  2√6 ” .

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    Now, let us simplify:  ” √12 ” :

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       ” √12  = ?  “

           12 = 4 * 3 ;

    So:  “√12 = √4 *√3  ” ;

        √4 * √3 = 2√3 ;

    So:  “√12 = √4 *√3 = 2√3 ” .

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    We are asked to solve—”simplify”— “√24 * √12 ” .

     √24 = 2√6 ; as we simplified above.

     √12 =  2√3  ; as we simplified above.

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    So:  ” √24 * √12 ” ;

         = 2√6  * 2√3 ;  

         = ?  ;  Note:  “2 * 2 = 4 ” ; and:  “√6 * √3 = √(6*3) = √18 ;

    So;    2√6  * 2√3 ;

         =  4√18 ;

    Now, we can simplify this value further:

       by simplifying:  ” √18 ” ;

           18 = 9 * 2 ;

    So:    ” √18 = √9 *√2  = 3 √2 ” ;

    So:  ” 4√18 = 4 * (3√2) =  12√2 ” .

         →  which  is our answer:  ” 12√2 ” .

        →  which corresponds to:  

         →  Answer choice:  [C]:  ” 12 * sq root 2 ” .  {or, write as:  ” 12√2 “.}.

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    Hope this answer and explanation is of help to you!

           Wishing you the best in your academic endeavors

                        — and within theBrainlycommunity!

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