Park Erickson
10/21/2023 · Senior High School
2. \( x=-\sqrt[4]{4}, y=-\sqrt[3]{3} \) ve \( z=-\sqrt[6]{8} \) veriliyor. Buna göre \( x, y \) ve \( z \) sayılarını küçükten büyüğe sıralayınız.
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Verilen sayıları hesaplayarak küçükten büyüğe sıralayalım:
1. **\( x = -\sqrt[4]{4} \)**:
\[
\sqrt[4]{4} = 4^{1/4} = (2^2)^{1/4} = 2^{2/4} = 2^{1/2} = \sqrt{2}
\]
Dolayısıyla,
\[
x = -\sqrt[4]{4} = -\sqrt{2} \approx -1.414
\]
2. **\( y = -\sqrt[3]{3} \)**:
\[
\sqrt[3]{3} \approx 1.442
\]
Dolayısıyla,
\[
y = -\sqrt[3]{3} \approx -1.442
\]
3. **\( z = -\sqrt[6]{8} \)**:
\[
\sqrt[6]{8} = 8^{1/6} = (2^3)^{1/6} = 2^{3/6} = 2^{1/2} = \sqrt{2}
\]
Dolayısıyla,
\[
z = -\sqrt[6]{8} = -\sqrt{2} \approx -1.414
\]
Şimdi bu değerleri karşılaştıralım:
- \( x \approx -1.414 \)
- \( y \approx -1.442 \)
- \( z \approx -1.414 \)
Küçükten büyüğe sıralama:
- \( y < z = x \)
Sonuç olarak, küçükten büyüğe sıralama:
\[
y < z = x
\]
Yani:
\[
-\sqrt[3]{3} < -\sqrt[6]{8} = -\sqrt[4]{4}
\]
Quick Answer
\[
y < z = x
\]
Yani:
\[
-\sqrt[3]{3} < -\sqrt[6]{8} = -\sqrt[4]{4}
\]
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