√20 + √80. explain how you got 6 from 20 

Let's break down how we simplify \( \sqrt{20} + \sqrt{80} \) step by step and arrive at an answer of 6.

### Step 1: Simplify each square root separately
We start by breaking down the numbers under the square roots into factors that include perfect squares.

1. \( \sqrt{20} \): 
   - \( 20 = 4 \times 5 \)
   - Since \( \sqrt{4} = 2 \), we can simplify:
   \[
   \sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}
   \]

2. \( \sqrt{80} \): 
   - \( 80 = 16 \times 5 \)
   - Since \( \sqrt{16} = 4 \), we can simplify:
   \[
   \sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}
   \]

### Step 2: Add the terms together
Now that we've simplified both square roots:

\[
\sqrt{20} + \sqrt{80} = 2\sqrt{5} + 4\sqrt{5}
\]

Since both terms have \( \sqrt{5} \) as a common factor, we can factor it out:

\[
2\sqrt{5} + 4\sqrt{5} = (2 + 4)\sqrt{5} = 6\sqrt{5}
\]

### Conclusion:
Thus, \( \sqrt{20} + \sqrt{80} = 6\sqrt{5} \). The answer involves the factor \( 6 \), but it remains multiplied by \( \sqrt{5} \), not just 6.

Do you want to know more about this concept or have any questions?

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Here are five related questions to explore:
1. How do you simplify square roots involving larger numbers?
2. How can you add or subtract square roots with different radicands?
3. What is the process to rationalize a square root denominator?
4. How do you estimate non-perfect square roots, such as \( \sqrt{5} \)?
5. What are other methods for simplifying radicals?

**Tip**: Always check for perfect square factors when simplifying square roots!

√20 + √80. explain how you got 6 from 20

This page explains how to simplify √20 + √80 by breaking down the radicals and adding them together. Learn the step-by-step process of simplifying square roots and understanding how the factor 6 comes into play. Ideal for students in Grades 8-10.

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