Exercises: Terms with Square Roots
What is the maximum domain of definition? If possible, write the term without a square root sign.
For this task you need the following basic knowledge: Square Roots
This expression is not defined whenever there is a negative number under the root.
Both exponents of and are even, so and are always positive or zero. Thus, the expression under the root is also positive or zero and the root is always defined:
Now, take the root.
You have to put dashes, since could be negative.
For this task you need the following basic knowledge: Square Roots
The root is net defined, if the expression under the root is negative. Now, squares of any number (also of ) are always positive of zero, so there are never any problems with the definition of the root.
Square .
For this task you need the following basic knowledge: Square Roots
The number under the root must not be negative. Only negative numbers or 0 are allowed for .
For this task you need the following basic knowledge: Square Roots
The number under the root must not be negative. However, the term in the squared bracket is always positive or zero, so we never have any problem with taking the root.
For this task you need the following basic knowledge: Square Roots
The number under the root must not be negative. However, squaring makes a term non-negative, so there is never a problem wit the root being defined.
For this task you need the following basic knowledge: Square Roots
The number under the root must not be negative. But since both squares are positive or zero, we never get any definition problems with the root.
It is not possible to further simplify this term. It is already in the simplest possible form.
For this task you need the following basic knowledge: Square Roots
Both and are never zero. The same holds for the product, so there are never any problems with definition of the square root.
Now, . Take the root. Root and square cancel each other out, but it is necessary to retain absolute values, since or might be negative and turned positive by the squaring.