Question
1) \( \sqrt{7} \cdot \sqrt{3} \)
Ask by Bradley Willis. in South Africa
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified form of \( \sqrt{7} \cdot \sqrt{3} \) is \( \sqrt{21} \).
Solution
To simplify the expression \( \sqrt{7} \cdot \sqrt{3} \), you can use the property of square roots that states:
\[
\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}
\]
Applying this property:
\[
\sqrt{7} \cdot \sqrt{3} = \sqrt{7 \times 3} = \sqrt{21}
\]
So, the simplified form of \( \sqrt{7} \cdot \sqrt{3} \) is:
\[
\sqrt{21}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
When you multiply square roots, you can combine them under a single radical. So, \( \sqrt{7} \cdot \sqrt{3} \) simplifies to \( \sqrt{21} \). It's like joining forces to create a new number! This property of square roots can make calculations much easier, especially when dealing with larger numbers. A common mistake is trying to directly multiply the numbers under the square root without realizing they can be combined first. Always remember that \( \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} \). This little mantra helps keep those pesky errors at bay!
