When to use absolute value in square root of a variable?

In the first example, the textbook says we need the absolute value symbol because x might be negative

In the second example, the textbook doesn't include the absolute value symbol

What's the difference? When do we use absolute value and when not?

Re: When to use absolute value in square root of a variable?

Quote:

Originally Posted by

**mathDad** In the first example, the textbook says we need the absolute value symbol because x might be negative

In the second example, the textbook doesn't include the absolute value symbol

What's the difference? When do we use absolute value and when not?

If memory serves the convention with the absolute value is only true for numbers. Using variables we would have .

Note that in the case of the odd power on the x forces the condition that so there is no need for the +/-.

-Dan

Re: When to use absolute value in square root of a variable?

Quote:

Originally Posted by

**topsquark** If memory serves the convention with the absolute value is only true for numbers. Using variables we would have

.

Note that in the case of

the odd power on the x forces the condition that

so there is no need for the +/-.

-Dan

Sorry Dan, but because .

However, is defined for therefore

As you correct observed for the odd case no absolute values are needed.

Re: When to use absolute value in square root of a variable?

Yes, in order that **exist** (we are talking about real numbers here) x itself must non-negative so |x|= x.

For example, in the first problem, , if x= 3 or -3, we would have as well as . To cover **both** possibilities we must say .

But in the second problem, , if x= -3, that would be which is not a real number.

Re: When to use absolute value in square root of a variable?

Quote:

Originally Posted by

**Plato** Sorry Dan, but

because

.

However,

is defined for

therefore

As you correct observed for the odd case no absolute values are needed.

Thanks for the catch.

-Dan

Re: When to use absolute value in square root of a variable?

(25)^1/2 = +/- 5

(25x^2)^1/2=+/- 5*abs value x

if x =-3

(25)*(-3)^2 =225

225^1/2 = +/- 15

Re: When to use absolute value in square root of a variable?

Quote:

Originally Posted by

**bjhopper** (25)^1/2 = +/- 5

(25x^2)^1/2=+/- 5*abs value x

if x =-3

(25)*(-3)^2 =225

225^1/2 = +/- 15

**That is simply **__incorrect__!

We have