Final answer:
Expression (a), 0 2√5, has a typo, but 2√5 is already simplified. Expression (b), 2/10, is not fully simplified as it can be reduced to 1/5. Expression (c), 4√5, cannot be simplified further and is presented in its simplest form.
Step-by-step explanation:
The simplification of mathematical expressions involves reducing them to their most basic form by performing operations such as multiplication, division, or changing the representation of numbers (for example, using exponents or roots). Let's consider the three expressions the student provided. Looking at option (a), 0 2√5, it seems there might be a typo, as it does not represent a common mathematical operation. However, we can make sense of the second part, 2√5, which is already simplified as it combines a rational number, 2, with the square root of an irrational number, √5.
Option (b), 2/10, can indeed be simplified further. This fraction can be reduced by dividing both numerator and denominator by their greatest common divisor, which is 2, resulting in 1/5. So, this expression is not already fully simplified.
Lastly, option (c), 4√5, is similar to (a) as it is an expression combining a rational number with the square root of an irrational number, and it cannot be simplified further without additional context or operations.
Integer Powers and Square Roots
Relating to the concept of integer powers and square roots, we know that x² = √x. Furthermore, using this knowledge, a fraction where the numerator and denominator are the same represents the number 1 since the two values cancel each other out.