Question 73887
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WHAT is the answer? square root of 32 times the square root of 144

{{{sqrt(32)sqrt(144)}}}

Break 32 and 144 down into prime factors

{{{32 = 8*4 = (4*2)(2*2) = (2*2*2)(2*2) = 2*2*2*2*2}}}

{{{ 144 = 12*12 = (4*3)(4*3) = ((2*2)*3)((2*2)*3) = 2*2*2*2*3*3}}}

So rewrite the problem as

{{{  sqrt(2*2*2*2*2)*sqrt(2*2*2*2*3*3)  }}}

Write all as one square root:

{{{  sqrt((2*2*2*2*2)(2*2*2*2*3*3))  }}}

{{{sqrt(2*2*2*2*2*2*2*2*2*3*3)}}}

Now pair up like factors which can be paired:

{{{sqrt((2*2)*(2*2)*(2*2)*(2*2)*2*(3*3))}}}

Write each pair of like factors as the square
of the factor

{{{sqrt((2^2)*(2^2)*(2^2)*(2^2)*2*(3^2))}}}

Now take individual square roots:

{{{sqrt(2^2)*sqrt(2^2)*sqrt(2^2)*sqrt(2^2)*sqrt(2)*sqrt(3^2)}}}

Now use the fact that the square root of the square of
a non-negative number is the non-negative number. 

{{{2*2*2*2*sqrt(2)*3 = 2*2*2*2*3*sqrt(2)= 
(2*2)*(2*2*3)*sqrt(2) = 4*(2*2*3)*sqrt(2) = 4*(4*3)*sqrt(2) = 4*12*sqrt(2) = 48sqrt(2)}}}

Edwin</pre>