Simplify the expression:
\((3\sqrt{200}) \times (4\sqrt{32})\)
Answer (3)
First let's see what we got
200 = 100 ∗ 2 = 10 2
and
32 = 2 5 = 2 4 ∗ 2 = 4 2
then
( 3 200 ) ∗ ( 4 32 )
replacing
3 ∗ ( 10 2 ) ∗ ( 4 ∗ 4 2 )
30 2 ∗ 16 2
480 ∗ 2 ∗ 2
480 ∗ 2
960
( 3 200 ) ⋅ ( 4 32 ) = ( 3 100 ⋅ 2 ) ⋅ ( 4 16 ⋅ 2 ) = ( 3 ⋅ 100 ⋅ 2 ) ⋅ ( 4 ⋅ 16 ⋅ 2 ) = = ( 3 ⋅ 10 ⋅ 2 ) ⋅ ( 4 ⋅ 4 ⋅ 2 ) = 3 ⋅ 10 ⋅ 4 ⋅ 4 ⋅ 2 ⋅ 2 = 480 ⋅ 2 ⋅ 2 = = 480 ⋅ 4 = 480 ⋅ 2 = 960
To simplify the expression ( 3 200 ) × ( 4 32 ) , we first simplify each square root to get 10 2 and 4 2 . Multiplying these results with their coefficients, we find the final answer to be 960 .
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