Question
10-Calcule a) \( \sqrt{2} \cdot \sqrt{7}= \) b) \( \sqrt[3]{5} \cdot \sqrt[3]{10}= \) c) \( \sqrt[4]{6} \cdot \sqrt[4]{2}= \) d) \( \sqrt{2}: \sqrt{18}= \) e) \( \sqrt{32} \cdot \sqrt{2}= \) f) \( \sqrt[5]{8} \cdot \sqrt[5]{4}= \) g) \( 2 \sqrt{3} \cdot 5 \sqrt{7}= \) L) \( 3 \sqrt{7} \cdot 2 \sqrt{5}= \) \( 2 \sqrt[3]{5} \cdot 3 \sqrt[3]{3}= \)
Ask by Lindsey Gross. in Brazil
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
a) \( \sqrt{14} \)
b) \( \sqrt[3]{50} \)
c) \( \sqrt[4]{12} \)
d) \( \frac{1}{3} \)
e) \( 8 \)
f) \( 2 \)
g) \( 10 \sqrt{21} \)
L) \( 6 \sqrt{35} \)
Último item: \( 6 \sqrt[3]{15} \)
Solution
a) Temos:
\[
\sqrt{2} \cdot \sqrt{7} = \sqrt{2 \cdot 7} = \sqrt{14}.
\]
b) Temos:
\[
\sqrt[3]{5} \cdot \sqrt[3]{10} = \sqrt[3]{5 \cdot 10} = \sqrt[3]{50}.
\]
c) Temos:
\[
\sqrt[4]{6} \cdot \sqrt[4]{2} = \sqrt[4]{6 \cdot 2} = \sqrt[4]{12}.
\]
d) Temos:
\[
\frac{\sqrt{2}}{\sqrt{18}} = \sqrt{\frac{2}{18}} = \sqrt{\frac{1}{9}} = \frac{1}{3}.
\]
e) Temos:
\[
\sqrt{32} \cdot \sqrt{2} = \sqrt{32 \cdot 2} = \sqrt{64} = 8.
\]
f) Temos:
\[
\sqrt[5]{8} \cdot \sqrt[5]{4} = \sqrt[5]{8 \cdot 4} = \sqrt[5]{32} = 2 \quad (\text{pois } 2^5 = 32).
\]
g) Temos:
\[
2 \sqrt{3} \cdot 5 \sqrt{7} = (2 \cdot 5)(\sqrt{3} \cdot \sqrt{7}) = 10 \sqrt{21}.
\]
L) Temos:
\[
3 \sqrt{7} \cdot 2 \sqrt{5} = (3 \cdot 2)(\sqrt{7} \cdot \sqrt{5}) = 6 \sqrt{35}.
\]
Último item:
\[
2 \sqrt[3]{5} \cdot 3 \sqrt[3]{3} = (2 \cdot 3)(\sqrt[3]{5} \cdot \sqrt[3]{3}) = 6 \sqrt[3]{15}.
\]
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Simplify this solution Beyond the Answer
To solve these expressions, let's break them down one at a time: a) \( \sqrt{2} \cdot \sqrt{7} = \sqrt{14} \) b) \( \sqrt[3]{5} \cdot \sqrt[3]{10} = \sqrt[3]{50} \) c) \( \sqrt[4]{6} \cdot \sqrt[4]{2} = \sqrt[4]{12} \) d) \( \sqrt{2} : \sqrt{18} = \frac{\sqrt{2}}{\sqrt{18}} = \frac{\sqrt{2}}{3\sqrt{2}} = \frac{1}{3} \) e) \( \sqrt{32} \cdot \sqrt{2} = \sqrt{64} = 8 \) f) \( \sqrt[5]{8} \cdot \sqrt[5]{4} = \sqrt[5]{32} = 2 \) g) \( 2 \sqrt{3} \cdot 5 \sqrt{7} = 10 \sqrt{21} \) h) \( 3 \sqrt{7} \cdot 2 \sqrt{5} = 6 \sqrt{35} \) i) \( 2 \sqrt[3]{5} \cdot 3 \sqrt[3]{3} = 6 \sqrt[3]{15} \) Hope that helps you with your calculations! Enjoy exploring the beauty of math!
