Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( (9 \sqrt{2})(5 \sqrt{2}) = 90 \)
Solution
To simplify the expression \( (9 \sqrt{2})(5 \sqrt{2}) \), follow these steps:
1. **Multiply the coefficients (numbers outside the radicals):**
\[
9 \times 5 = 45
\]
2. **Multiply the radicals (\(\sqrt{2} \times \sqrt{2}\)):**
\[
\sqrt{2} \times \sqrt{2} = \sqrt{2 \times 2} = \sqrt{4} = 2
\]
3. **Combine the results:**
\[
45 \times 2 = 90
\]
**Final Answer:**
\[
(9 \sqrt{2})(5 \sqrt{2}) = 90
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
First, let's multiply the numerical coefficients: \(9 \times 5 = 45\). Next, we handle the square root parts: \(\sqrt{2} \times \sqrt{2} = \sqrt{4} = 2\). Now, we can combine both results: \(45 \times 2 = 90\). So, the answer is \(90\). Now, isn't it fun how multiplying square roots works out like a magic trick? Once you get the hang of combining coefficients and square roots, math becomes a lot more playful. Plus, this skill is not just for the classroom – you’ll see it pop up anytime you deal with expressions in algebra or geometry!
