Find the product of 12−−√ and 5/6. What type of number is it?
To find the product, we multiply 12−−√ by 5/6.
(12−−√)(5/6) can be written as (12√(−1))(5/6).
We can simplify this expression by rewriting √(−1) as "i", where i represents the imaginary unit.
So, (12−−√)(5/6) becomes (12i)(5/6).
To multiply complex numbers, we multiply the real parts and the imaginary parts separately.
In this case, the real parts are 12 and 5/6, and the imaginary parts are i.
Multiplying the real parts gives us (12)(5/6) = 60/6 = 10.
Multiplying the imaginary parts gives us i.
Therefore, the product of 12−−√ and 5/6 is 10i.
So, the product is a complex number.
To find the product of 12−−√ and 5/6, we simply multiply the two numbers together.
12−−√ × 5/6
To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is 6.
(12−−√ × 5)/(6 × 6)
(12−−√ × 5) / 36
To multiply (12−−√ × 5), we multiply the whole number and the fractional part separately.
12 × 5 = 60
−−√ × 5 = 5√2
So, the product is 60 + 5√2.
Now, let's determine the type of number it is.
The number 60 is a rational number because it can be expressed as a fraction (60/1).
The number 5√2 is an irrational number because it cannot be expressed as a fraction and has an irrational component (√2).
Therefore, the product of 12−−√ and 5/6 is a combination of a rational number and an irrational number, which makes it an irrational number.