Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
Let's find the cube roots of the given fractions step by step.
### a) [tex]\( \frac{8}{27} \)[/tex]
To find the cube root of [tex]\( \frac{8}{27} \)[/tex], we'll take the cube root of the numerator and the cube root of the denominator separately.
- The cube root of 8:
[tex]\[ \sqrt[3]{8} = 2 \][/tex]
- The cube root of 27:
[tex]\[ \sqrt[3]{27} = 3 \][/tex]
Thus, the cube root of [tex]\( \frac{8}{27} \)[/tex] is:
[tex]\[ \frac{\sqrt[3]{8}}{\sqrt[3]{27}} = \frac{2}{3} \][/tex]
### b) [tex]\( \frac{64}{125} \)[/tex]
Next, for [tex]\( \frac{64}{125} \)[/tex]:
- The cube root of 64:
[tex]\[ \sqrt[3]{64} = 4 \][/tex]
- The cube root of 125:
[tex]\[ \sqrt[3]{125} = 5 \][/tex]
Thus, the cube root of [tex]\( \frac{64}{125} \)[/tex] is:
[tex]\[ \frac{\sqrt[3]{64}}{\sqrt[3]{125}} = \frac{4}{5} \][/tex]
### c) [tex]\( \frac{125}{216} \)[/tex]
Now, for [tex]\( \frac{125}{216} \)[/tex]:
- The cube root of 125:
[tex]\[ \sqrt[3]{125} = 5 \][/tex]
- The cube root of 216:
[tex]\[ \sqrt[3]{216} = 6 \][/tex]
Thus, the cube root of [tex]\( \frac{125}{216} \)[/tex] is:
[tex]\[ \frac{\sqrt[3]{125}}{\sqrt[3]{216}} = \frac{5}{6} \][/tex]
### d) [tex]\( \frac{343}{1728} \)[/tex]
Finally, for [tex]\( \frac{343}{1728} \)[/tex]:
- The cube root of 343:
[tex]\[ \sqrt[3]{343} = 7 \][/tex]
- The cube root of 1728:
[tex]\[ \sqrt[3]{1728} = 12 \][/tex]
Thus, the cube root of [tex]\( \frac{343}{1728} \)[/tex] is:
[tex]\[ \frac{\sqrt[3]{343}}{\sqrt[3]{1728}} = \frac{7}{12} \][/tex]
In conclusion, the cube roots of the given fractions are:
a) [tex]\( \frac{2}{3} \)[/tex]
b) [tex]\( \frac{4}{5} \)[/tex]
c) [tex]\( \frac{5}{6} \)[/tex]
d) [tex]\( \frac{7}{12} \)[/tex]
### a) [tex]\( \frac{8}{27} \)[/tex]
To find the cube root of [tex]\( \frac{8}{27} \)[/tex], we'll take the cube root of the numerator and the cube root of the denominator separately.
- The cube root of 8:
[tex]\[ \sqrt[3]{8} = 2 \][/tex]
- The cube root of 27:
[tex]\[ \sqrt[3]{27} = 3 \][/tex]
Thus, the cube root of [tex]\( \frac{8}{27} \)[/tex] is:
[tex]\[ \frac{\sqrt[3]{8}}{\sqrt[3]{27}} = \frac{2}{3} \][/tex]
### b) [tex]\( \frac{64}{125} \)[/tex]
Next, for [tex]\( \frac{64}{125} \)[/tex]:
- The cube root of 64:
[tex]\[ \sqrt[3]{64} = 4 \][/tex]
- The cube root of 125:
[tex]\[ \sqrt[3]{125} = 5 \][/tex]
Thus, the cube root of [tex]\( \frac{64}{125} \)[/tex] is:
[tex]\[ \frac{\sqrt[3]{64}}{\sqrt[3]{125}} = \frac{4}{5} \][/tex]
### c) [tex]\( \frac{125}{216} \)[/tex]
Now, for [tex]\( \frac{125}{216} \)[/tex]:
- The cube root of 125:
[tex]\[ \sqrt[3]{125} = 5 \][/tex]
- The cube root of 216:
[tex]\[ \sqrt[3]{216} = 6 \][/tex]
Thus, the cube root of [tex]\( \frac{125}{216} \)[/tex] is:
[tex]\[ \frac{\sqrt[3]{125}}{\sqrt[3]{216}} = \frac{5}{6} \][/tex]
### d) [tex]\( \frac{343}{1728} \)[/tex]
Finally, for [tex]\( \frac{343}{1728} \)[/tex]:
- The cube root of 343:
[tex]\[ \sqrt[3]{343} = 7 \][/tex]
- The cube root of 1728:
[tex]\[ \sqrt[3]{1728} = 12 \][/tex]
Thus, the cube root of [tex]\( \frac{343}{1728} \)[/tex] is:
[tex]\[ \frac{\sqrt[3]{343}}{\sqrt[3]{1728}} = \frac{7}{12} \][/tex]
In conclusion, the cube roots of the given fractions are:
a) [tex]\( \frac{2}{3} \)[/tex]
b) [tex]\( \frac{4}{5} \)[/tex]
c) [tex]\( \frac{5}{6} \)[/tex]
d) [tex]\( \frac{7}{12} \)[/tex]
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.