https://file.aiquickdraw.com/mathbot/file/1726847080960vkwzmp47.jpg

The expression in the image is:

\[
\frac{5 \sqrt{7} \times \sqrt{3}}{\sqrt{28}}
\]

Let’s simplify this step-by-step:

### Step 1: Multiply the square roots in the numerator
\[
\sqrt{7} \times \sqrt{3} = \sqrt{7 \times 3} = \sqrt{21}
\]

Now the expression becomes:
\[
\frac{5 \sqrt{21}}{\sqrt{28}}
\]

### Step 2: Simplify the square roots in the denominator
We can simplify \(\sqrt{28}\). Since \(28 = 4 \times 7\), we have:
\[
\sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7} = 2\sqrt{7}
\]

So the expression is now:
\[
\frac{5 \sqrt{21}}{2 \sqrt{7}}
\]

### Step 3: Simplify the fraction
We can cancel out \(\sqrt{7}\) from both the numerator and denominator, as \(\sqrt{21} = \sqrt{7 \times 3}\) contains a factor of \(\sqrt{7}\):
\[
\frac{5 \sqrt{21}}{2 \sqrt{7}} = \frac{5 \sqrt{7 \times 3}}{2 \sqrt{7}} = \frac{5 \sqrt{3}}{2}
\]

### Final Answer:
\[
\frac{5 \sqrt{3}}{2}
\]

Would you like any further clarification or details? Here are some additional questions to explore:

1. What are the properties of square roots that allow simplification like \(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\)?
2. How do you simplify fractions involving radicals in both the numerator and denominator?
3. Can we use rationalization to simplify such expressions further?
4. How can prime factorization help in simplifying square roots like \(\sqrt{28}\)?
5. What are the rules for multiplying and dividing radicals?

**Tip:** Always check if square roots can be simplified by breaking them into factors involving perfect squares.

Simplify the expression (5√7 × √3) / √28

Learn how to simplify the radical expression (5√7 × √3) / √28. This detailed solution covers key concepts such as the multiplication and division of radicals and simplifying square roots.

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