To which set(s) of numbers does the number sqrt -16 belong? Select all that apply.
real numbers
complex numbers***
rational numbers
imaginary numbers***
irrational numbers
I can only pick two, and that's what I think it is. Please check? Thanks
correct
You are correct
Yes, you are correct. The number √(-16) would belong to the set of complex numbers and imaginary numbers. The square root of a negative number is considered an imaginary number, and all complex numbers, including imaginary numbers, are subsets of the real numbers. Therefore, it belongs to both the complex numbers and the imaginary numbers.
To determine which sets of numbers the number √(-16) belongs to, let's break it down step by step:
1. Real numbers: Real numbers include all rational and irrational numbers. In this case, since the number √(-16) involves an imaginary component (√-1), it cannot belong to the set of real numbers.
2. Complex numbers: Complex numbers include both real and imaginary numbers. Complex numbers are expressed in the form a + bi, where "a" is the real part and "bi" is the imaginary part. The number √(-16) can be written as 4i, where 4 is the imaginary part (i.e., 4 * √(-1)). Therefore, √(-16) belongs to the set of complex numbers.
3. Rational numbers: Rational numbers are numbers that can be expressed as a ratio of two integers. Since the number √(-16) cannot be expressed as a ratio of two integers, it does not belong to the set of rational numbers.
4. Imaginary numbers: Imaginary numbers are numbers expressed as a multiple of the imaginary unit i, where i = √(-1). Since √(-16) is a multiple of √(-1) (i.e., 4i), √(-16) belongs to the set of imaginary numbers.
5. Irrational numbers: Irrational numbers cannot be expressed as a fraction or a ratio of two integers. Since √(-16) is not irrational, it does not belong to the set of irrational numbers.
Based on the above analysis, the number √(-16) belongs to the sets of complex numbers and imaginary numbers.