Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\sqrt{18} = 3\sqrt{2} \approx 4.2426
\]
Solution
To simplify and evaluate \( \sqrt{18} \), follow these steps:
### 1. Simplify the Square Root
First, factor 18 into its prime components:
\[
18 = 9 \times 2 = 3^2 \times 2
\]
Now, use the property of square roots that \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \):
\[
\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}
\]
So, the simplified form of \( \sqrt{18} \) is:
\[
\sqrt{18} = 3\sqrt{2}
\]
### 2. Decimal Approximation
To find the decimal value, calculate \( \sqrt{2} \) first:
\[
\sqrt{2} \approx 1.4142
\]
Then multiply by 3:
\[
3 \times 1.4142 \approx 4.2426
\]
So,
\[
\sqrt{18} \approx 4.2426
\]
### **Final Answer**
\[
\sqrt{18} = 3\sqrt{2} \approx 4.2426
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
Did you know that \( \sqrt{18} \) can be simplified? It breaks down to \( \sqrt{9 \times 2} \), which is \( \sqrt{9} \times \sqrt{2} = 3\sqrt{2} \). This little trick of simplifying square roots can help make calculations simpler and neater, especially in algebra! In real-world applications, simplifying square roots helps in fields such as engineering and physics, where precise measurements are crucial. For example, if you're calculating the diagonal distance across a rectangular area using the Pythagorean theorem, simplifying square roots allows for easier representation and accurate estimations, making your work less cluttered and more precise!
