express in simplest radical form: 5 , square root of 72 - square root of 98

To express \( 5\sqrt{72} - \sqrt{98} \) in its simplest radical form, we need to first simplify the square roots and then combine the terms if possible.

### Step 1: Simplify the square roots
1. \(\sqrt{72}\)
   \[
   \sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}
   \]
   So, \(5\sqrt{72}\) becomes:
   \[
   5 \times 6\sqrt{2} = 30\sqrt{2}
   \]

2. \(\sqrt{98}\)
   \[
   \sqrt{98} = \sqrt{49 \times 2} = \sqrt{49} \times \sqrt{2} = 7\sqrt{2}
   \]
   So, \(-\sqrt{98}\) becomes:
   \[
   -7\sqrt{2}
   \]

### Step 2: Combine the simplified terms
Now, combine \(30\sqrt{2}\) and \(-7\sqrt{2}\):
\[
30\sqrt{2} - 7\sqrt{2} = 23\sqrt{2}
\]

### Final Answer
The expression in its simplest radical form is:
\[
\boxed{23\sqrt{2}}
\]

Would you like any further details or have any questions?

Here are 5 related questions you might find interesting:
1. How do you simplify square roots that involve products of prime factors?
2. What are some common mistakes when simplifying radical expressions?
3. How do you add or subtract radicals with different radicands?
4. What is the importance of identifying perfect squares when simplifying square roots?
5. Can radicals always be combined? Under what circumstances?

**Tip:** When simplifying expressions with radicals, always ensure that the radicand is expressed in its simplest form by factoring out perfect squares.

Learn how to simplify the radical expression 5 times the square root of 72 minus the square root of 98 with a step-by-step solution. This problem covers radical expressions, simplifying square roots, and combining radical terms. Suitable for high school students in Grades 9-12.

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