## 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

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

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

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

The answer is C) .

Step-by-step explanation:

For a real number , .

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

How does this rule apply here? .

Similarly, .

That is: .

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→   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!