Exercises: Terms with Square Roots
For which numbers are the terms defined? Write them without square roots and think about whether an absolute value is necessary or not.
For this task you need the following basic knowledge: Square Roots
Determine the domain of definition
First determine the domain of definition.
Only positive expressions are allowed under the root, therefore only positive values or 0 may be used for .
Write the term without square roots
Conclude the roots with the calculation rules for square roots.
↓ Conclude everything below the root.
↓ Take the square root and do not forget the absolute value.
↓ Conclude and consider whether you can omit the absolute value.
For this task you need the following basic knowledge: Square Roots
Determine the domain of definition
First determine the domain of definition.
Only positive expressions are allowed under the root.
The first root in the numerator is always positive because the variable is squared.
However, in the second root of the numerator you may only insert positive values or 0 for .
The same applies to the root in the denominator, but here must be greater than zero.
Therefore only positive values or 0 may be used for .
, also
Write the term without square roots
Conclude the roots with the calculation rules for square roots.
↓ Conclude everything below the root.
↓ Take the square root and do not forget the absolute value.
↓ Conclude and consider whether you can omit the absolute value.
For this task you need the following basic knowledge: Square Roots
Determine the domain of definition
First determine the domain of definition.
Only positive expressions are allowed under the root. This gives you the following condition:
Write the term without square roots
Take the square root and do not forget the absolute value.
For this task you need the following basic knowledge: Square Roots
Determine the domain of definition
First determine the domain of definition.
Only positive expressions are allowed under the root. Since the term under the root is squared, it will always be positive. So there are no definition problems, no matter which values you use for .
Write the term without square roots
↓ Consider whether you can omit the absolute value.