I need help with my algebra 3 homework please!?

Question

the square root of nine times the square root of 96. my answer was 2square root of 2 times 4square root of 6

Answer 1

i got about 29.37

Answer 2

The square root of nine is simple enough.  It's three.  A perfect square.

The square root of 96 isn't quite so simple.  I'd recommend factoring that number as much as you can.

I find the prime factorization to be  3 * 2^5.  Or, 3 * 2 * 2^4.  And, the square root of 2^4 is 2^2, or simply 4

So, the square root of 96 is   four times the square root of six

Three, times four times the square root of six, is twelve times the square root of six.

English is clumsy for math.  Lemme see if I can make that clearer.

√( 9 ) * √( 96 )

3 * √( 96 )

3 * √( 16 * 6 )

3 * √( 16 ) * √( 6 )

3 * 4 * √( 6 )

12 * √( 6 )

12√( 6 )

Twelve square roots of six

oh, wait.  Are we assuming that the square root of a number is the positive square root of that number?  If we are, that's ok.  If we're not, then the square root of nine is positive-or-negative three, and the square root of sixteen is positive-or-negative sixteen, and our final answer would be

±12√( 6 )

Or, did you mean the square root of the quantity nine times the square root of six?

√[ 9 * √( 96 ) ]

√[ 9 * √( 16 * 6 ) ]

√[ 9 * 4 * √( 6 ) ]

√[ 36 *  Ã¢ÂˆÂš( 6 ) ]

Hmm, I don't have a fourth root symbol in this font.

6 * ^4√( 6 )

or, maybe

6 * 6^(1/4)

Six fourth roots of six

Wow.  Math is easier with the English outta the way.

Answer 3

sqrt 9 x sqrt 96 =

3 x sqrt (16 x 6) =

3 x 4 sqrt 6 =

12 sqrt 6

Answer 4

+/- 3 * 4√6

Answer 5

Square root of 9 is 3.

Square root of 96 is 9.7979

Multiply them together for your answer.....something around 29...something