Question

how to find the cube root of 2

Answer 1

cube root of 2 is 1.25992104989
and I don't know how to find it

Answer 2

For approximating cube root of 2 :

• First estimate must be 1

$\because \lfloor \sqrt[3]{2} \rfloor = 1$

For calculating Decimal Digits

• First estimate ≤ 10/3 ≈3.33

As,

$728 \leq 1000 < 1197$

Therefore, First digit after decimal is 2

• Second estimate ≤ 2720/432≈6.29

Thus, We can approximate

$\sqrt[3]{2} \approx1.26$

Verification

$1.26 {}^{3} = 2.000376 \approx2$

is a quite good approximation.