Simplify completely: 9radical5-14radical5+18radical5

Answer =

Let's simplify the given expression:

\[
9\sqrt{5} - 14\sqrt{5} + 18\sqrt{5}
\]

Since all the terms involve \(\sqrt{5}\), we can factor out the \(\sqrt{5}\):

\[
(9 - 14 + 18)\sqrt{5}
\]

Now, simplify the coefficients inside the parentheses:

\[
9 - 14 + 18 = 13
\]

So the expression becomes:

\[
13\sqrt{5}
\]

Thus, the simplified expression is:

\[
\boxed{13\sqrt{5}}
\]

Would you like any further details or explanations?

Here are 5 related questions to explore:
1. How do you simplify expressions with different radicals?
2. What happens when radicals have different values under the square root?
3. Can you add or subtract radicals with different coefficients?
4. What is the process to simplify an expression like \(3\sqrt{2} + 5\sqrt{2} - 2\sqrt{2}\)?
5. How do you handle multiplication involving radicals?

**Tip:** Always ensure the radicands (numbers under the square root) are the same before combining like radical terms.

Simplify completely: 9radical5-14radical5+18radical5

Learn how to simplify the expression 9√5 - 14√5 + 18√5 step by step. This guide covers the addition and subtraction of like radicals, showing the complete simplification process, making it ideal for students in Grades 8-10.

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