Question

When adding 10 to the square root of a number and -9, which type of number is the sum?

a) Real number
b) Imaginary number
c) Complex number
d) Irrational number

Answer 1

The sum can be a real number (option a), an irrational number (option d), or both.

Step-by-step explanation:

The sum of adding 10 to the square root of a number and -9 can be any type of number. It depends on the number you start with. Let's look at the possible types of numbers:

1. If the number is a perfect square, like 4 or 25, then the square root is a rational number. Adding 10 to a rational number results in a rational number.
2. If the number is not a perfect square, like 2 or 7, then the square root is an irrational number. Adding 10 to an irrational number gives a sum that is also irrational.
3. If the number is negative, the square root doesn't exist in the set of real numbers. In this case, adding 10 to -9 gives a sum that is a real number.

So, depending on the number you start with, the sum can be a real number (option a), an irrational number (option d), or both.