Question
ADDITION AND SUBTRACTION OF RADICALS (Show your Solution) \( \begin{array}{ll}1.3 \sqrt{6}+6 \sqrt{6}+8 \sqrt{6}+4 \sqrt{6} & 2.4 \sqrt{a b}+2 \sqrt{a b}+5 \sqrt{a b}+11 \sqrt{a b}\end{array} \)
Ask by Harper Bowers. in the Philippines
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 19.3 \sqrt{6} \) and \( 22 \sqrt{a b} \)
Solution
To solve the addition and subtraction of radicals, we will combine like terms. Like terms are those that have the same radical part.
### Problem 1: \( 1.3 \sqrt{6} + 6 \sqrt{6} + 8 \sqrt{6} + 4 \sqrt{6} \)
1. **Identify the like terms**: All terms contain \( \sqrt{6} \).
2. **Combine the coefficients**:
\[
1.3 + 6 + 8 + 4
\]
Let's calculate this step by step:
- First, add \( 1.3 + 6 = 7.3 \)
- Next, add \( 7.3 + 8 = 15.3 \)
- Finally, add \( 15.3 + 4 = 19.3 \)
3. **Write the final result**:
\[
19.3 \sqrt{6}
\]
### Problem 2: \( 4 \sqrt{a b} + 2 \sqrt{a b} + 5 \sqrt{a b} + 11 \sqrt{a b} \)
1. **Identify the like terms**: All terms contain \( \sqrt{a b} \).
2. **Combine the coefficients**:
\[
4 + 2 + 5 + 11
\]
Let's calculate this step by step:
- First, add \( 4 + 2 = 6 \)
- Next, add \( 6 + 5 = 11 \)
- Finally, add \( 11 + 11 = 22 \)
3. **Write the final result**:
\[
22 \sqrt{a b}
\]
### Final Answers:
1. \( 19.3 \sqrt{6} \)
2. \( 22 \sqrt{a b} \)
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Simplify this solution Extra Insights
Let’s break down the additions and simplify step by step for both problems. 1. For \( 1.3 \sqrt{6} + 6 \sqrt{6} + 8 \sqrt{6} + 4 \sqrt{6} \): - First, combine the coefficients (the numbers in front of the radicals): \( 1.3 + 6 + 8 + 4 = 19.3 \). - So, the simplified expression is: \[ 19.3 \sqrt{6} \] 2. For \( 4 \sqrt{a b} + 2 \sqrt{a b} + 5 \sqrt{a b} + 11 \sqrt{a b} \): - Similarly, add the coefficients: \( 4 + 2 + 5 + 11 = 22 \). - Thus, the simplified expression becomes: \[ 22 \sqrt{a b} \] Putting it all together, the final results are: 1. \( 19.3 \sqrt{6} \) 2. \( 22 \sqrt{a b} \)
