# Root question: true or false? "a+b (a+b is in root) is defined for -b <= a"

#### Joacro

##### New member
Root question: true or false? "a+b (a+b is in root) is defined for -b <= a"

Hi there I am busy with an assignment and would appreciate some help

Could someone please tell me if the following is true

a+b (a+b is in root) is defined for -b smaller and equal to a

Regards

#### mmm4444bot

##### Super Moderator
Staff member
Could someone please tell me if the following is true

a+b (a+b is in root) is defined for -b smaller and equal to a

The word "and" is wrong. It needs to be "or".

Can you see why?
This exercise is not worded as well as it could be, but I understand what they're trying to ask.

Consider the expression sqrt(a + b), where symbol a represents some positive number and symbol b represents a negative number. Is the following statement true or false?

sqrt(a + b) is defined when the absolute value of b is less than or equal to a.

Here's a hint to think about. In the Real number system, can we take the square root of a negative quantity?

For example, does the number sqrt(-16) exist, in the Real number system?

Here's another hint. What happens to the value of a+b when the absolute value of b is greater than a?

If you don't know the meaning of the phrases "absolute value" or "Real number system", let us know. We can explain the exercise a different way. :cool: