https://file.aiquickdraw.com/mathbot/file/172558726061878xbepx1.jpg

The expression provided in the image is:

\[
\frac{15}{\sqrt{5}} - \sqrt{20}
\]

Let's simplify this expression step by step.

### Step 1: Simplify \(\frac{15}{\sqrt{5}}\)
We rationalize the denominator by multiplying both the numerator and denominator by \(\sqrt{5}\):

\[
\frac{15}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{15\sqrt{5}}{5} = 3\sqrt{5}
\]

### Step 2: Simplify \(\sqrt{20}\)
The square root of 20 can be broken down as:

\[
\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}
\]

### Step 3: Combine the terms
Now, substitute the simplified terms:

\[
3\sqrt{5} - 2\sqrt{5} = \sqrt{5}
\]

### Final Answer:
The simplified expression is:

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

Would you like further clarification on any steps? Feel free to ask!

Here are 5 related questions to deepen your understanding:

1. How do you rationalize a denominator with a square root?
2. Why does \(\sqrt{20}\) simplify to \(2\sqrt{5}\)?
3. How do you add and subtract radical expressions like \(3\sqrt{5} - 2\sqrt{5}\)?
4. What are other ways to simplify square roots of larger numbers?
5. Can all radical expressions be simplified in a similar way?

**Tip:** Always look for perfect square factors when simplifying square roots, as it makes the process easier.

Learn how to simplify the expression 15 divided by the square root of 5 minus the square root of 20. This step-by-step guide breaks down rationalizing denominators and simplifying radicals. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation