Question

Find the cube roots of rational numbers:-686/-2662

Answer 1

Answer:

7/11

Step-by-step explanation:

If x and a are two rational numbers such that x³= a then we will say that x is the cube root of a and we will write - ³√a

Thus, to find the cube root of any number we use the formula -

∛(a/b) = (∛a)/(∛b)

Thus,

-686/-2662

= 343/1331

= (∛343)/(∛1331)

= (∛7 x 7 x 7)/(∛11 x 11 x 11 )

= 7/11

Thus the cube root of 686/2882 is 7/11

Answer 2

Answer:

$\left(\sqrt[3]{\frac{-686}{-2662}}\right)= \frac{7}{11}$

Step-by-step explanation:

$\left(\sqrt[3]{\frac{-686}{-2662}}\right)\\=\left(\sqrt[3]{\frac{2\times 343}{2\times 1331}}\right)\\=\left(\sqrt[3]{\frac{ 7^{3}}{11^{3}}}\right)\\=\left(\sqrt[3]{\big(\frac{ 7}{11}\big)^{3}}}\right)\\=\frac{7}{11}$

Therefore,

$\left(\sqrt[3]{\frac{-686}{-2662}}\right)= \frac{7}{11}$

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