To simplify the expression \(\frac{\sqrt{140}}{\sqrt{77}}\), we can combine the square roots:

\[
\frac{\sqrt{140}}{\sqrt{77}} = \sqrt{\frac{140}{77}}
\]

Next, simplify the fraction inside the square root:

\[
\frac{140}{77} = \frac{140 \div 7}{77 \div 7} = \frac{20}{11}
\]

So the expression becomes:

\[
\sqrt{\frac{20}{11}} = \frac{\sqrt{20}}{\sqrt{11}}
\]

Finally, simplify \(\sqrt{20}\) as much as possible:

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

Thus, the expression is:

\[
\frac{2\sqrt{5}}{\sqrt{11}}
\]

This is the simplified form of the given expression.

Would you like more details or have any questions?

---

Here are five related questions you might find interesting:

1. How would you rationalize the denominator in \(\frac{2\sqrt{5}}{\sqrt{11}}\)?
2. What is the simplified form of \(\frac{\sqrt{50}}{\sqrt{2}}\)?
3. How do you simplify \(\frac{\sqrt{72}}{\sqrt{18}}\)?
4. What is the value of \(\sqrt{\frac{7}{2}}\) in its simplest form?
5. Can you simplify the expression \(\frac{\sqrt{8}}{\sqrt{3}}\)?

**Tip:** When simplifying square roots, always look for perfect square factors to reduce the expression.

Learn how to simplify the expression √140/√77 with a detailed step-by-step solution. This problem covers key mathematical concepts such as square root simplification and fraction simplification. Suitable 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