Final answer:
To show that \(\frac{n}{100}\) is not equal to \(\sqrt{n}\), we can compare these expressions for any arbitrary positive number n. Using n = 100 as an example, \(\frac{100}{100} = 1\) while \(\sqrt{100} = 10\), demonstrating that they are not equivalent.
Step-by-step explanation:
To prove that \(\frac{n}{100}\) is not equal to \(\sqrt{n}\), we can explore these expressions in the context of basic algebraic manipulation.
For the expression \(\frac{n}{100}\), this represents a hundredth of a number. The square root of a number, \(\sqrt{n}\), represents a value that, when multiplied by itself, gives the original number n.
Let us take an arbitrary positive number n and analyze both expressions:
- \(\frac{n}{100}\) simplifies to a reduced form of the original number;
- While \(\sqrt{n}\) provides a number which, when squared, gives the original number back.
Without invoking limits or involving unnecessary complexity, we can use a counter-example to illustrate the point:
- Let n = 100;
- Then \(\frac{100}{100} = 1\);
- And \(\sqrt{100} = 10\);
It's clear from the counter-example that 1 is not equal to 10, illustrating that \(\frac{n}{100}\) is indeed not equal to \(\sqrt{n}\) in a general sense. This basic comparison is sufficient to conclude that the two expressions are not equivalent.