Find the product of 12−−√ and 56. What type of number is it?
The product of 12−−√ and 56 is (12−−√)(56).
To find the product, we can simplify the square root of 12. Since 12 is a perfect square, the square root is a rational number. The square root of 12 is approximately 3.464.
So, (12−−√)(56) is equal to (3.464)(56) = 193.504.
The product, 193.504, is a rational number.
To find the product of 12−−√ and 56, we simply multiply these two numbers together.
12−−√ * 56 = (sqrt(12)) * 56
We can simplify sqrt(12) as follows:
sqrt(12) = sqrt(4 * 3) = sqrt(4) * sqrt(3) = 2 * sqrt(3)
Substituting this back into our equation:
(2 * sqrt(3)) * 56 = 112 * sqrt(3)
So, the product of 12−−√ and 56 is 112 * sqrt(3).
As for the type of number it is, 112 * sqrt(3) is an irrational number, because it involves the square root of a non-perfect square (3).