Question
\( \begin{array}{rc}\text { b) } 6+5 \sqrt{5}+3-2 \sqrt{5} & {[2 \text { marks }](5)} \\ & \text { Section Two - Algebra }\end{array} \)
Ask by Phillips Coles. in the United Kingdom
Mar 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( 9 + 3\sqrt{5} \).
Solution
To simplify the expression \( 6 + 5\sqrt{5} + 3 - 2\sqrt{5} \), we can follow these steps:
1. **Combine the constant terms**: Identify and add the constant numbers together.
2. **Combine the terms with \(\sqrt{5}\)**: Identify and combine the coefficients of \(\sqrt{5}\).
Let's perform these steps:
1. **Combine the constant terms**:
\[
6 + 3 = 9
\]
2. **Combine the terms with \(\sqrt{5}\)**:
\[
5\sqrt{5} - 2\sqrt{5} = (5 - 2)\sqrt{5} = 3\sqrt{5}
\]
Now, we can put it all together:
\[
9 + 3\sqrt{5}
\]
Thus, the simplified expression is:
\[
\boxed{9 + 3\sqrt{5}}
\]
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Simplify this solution Bonus Knowledge
Combining like terms in the expression \(6 + 5\sqrt{5} + 3 - 2\sqrt{5}\) is key to simplifying it. Start by adding the constant terms, which are \(6\) and \(3\) to get \(9\). Next, combine the like terms involving \(\sqrt{5}\): \(5\sqrt{5} - 2\sqrt{5} = 3\sqrt{5}\). So, the simplified expression is \(9 + 3\sqrt{5}\). Algebraic expressions like this one often pop up in real-world situations such as physics or engineering, where variables represent quantities that might change. Simplifying expressions allows for easier calculations, making it crucial in situations ranging from budgeting in finance to solving for forces in mechanics.
