rationalize the denominator and simplify.  √ 140 / √ 5

We are given the expression:

\[
\frac{\sqrt{140}}{\sqrt{5}}
\]

### Step 1: Combine the square roots
We can combine the square roots into one by using the property \(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\):

\[
\frac{\sqrt{140}}{\sqrt{5}} = \sqrt{\frac{140}{5}}
\]

### Step 2: Simplify the fraction inside the square root
Next, simplify \(\frac{140}{5}\):

\[
\frac{140}{5} = 28
\]

So, the expression becomes:

\[
\sqrt{28}
\]

### Step 3: Simplify the square root
Now, simplify \(\sqrt{28}\). We can factor 28 as:

\[
28 = 4 \times 7
\]

Thus:

\[
\sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7} = 2\sqrt{7}
\]

### Final Answer:
The simplified form of \(\frac{\sqrt{140}}{\sqrt{5}}\) is:

\[
2\sqrt{7}
\]

Would you like more details or have any questions? Here are 5 related questions:

1. How do you rationalize the denominator when variables are involved?
2. What is the property of square roots that allows combining them as a single fraction?
3. How do you simplify square roots with higher powers, such as cube roots?
4. What are the key steps in simplifying radical expressions?
5. Can you explain how to deal with square roots in polynomial expressions?

**Tip:** Always try to factor out perfect squares when simplifying square roots to make your work easier!

rationalize the denominator and simplify. √140 / √5

Learn how to rationalize the denominator and simplify the expression √140 / √5. This step-by-step solution demonstrates how to combine square roots, simplify radicals, and factor numbers for easy understanding. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation