Question

You are told that $1,331$ is a perfect cube. Can you guess without factorization what is its cube root? Similarly, guess the cube roots of $4913,12167,32768$.

Answer 1

(i) Separating the given number (1331) into two groups:

$1331\to 1$ and $331$

$\because$ 331 ends in 1

$\therefore$ Unit's digit of the cube root $=1$

$\because 1^3=1$ and $\sqrt[1]{11}$

$\therefore$ Ten's digit of the cube root $=1$

$\therefore \sqrt[3]{31331}=11$

(ii) Separating the given number (4913) into two groups:

$4913\to 4$ and $931$

Unit's digit:

$\because$ Unit's digit in 913 is 3

$\therefore$ Unit's digit of the cube root $=7$

$\because 7^3=343$ which end in 3

Ten's digit:

$\because 1^3=1,2^3=8$

and $1<4<8$

i.e $1^3<4<2^3$

$\therefore$ Ten's digit of the cube root is 1

$\therefore \sqrt[3]{34913}=17$

(iii) Separating the given number (12167) into two groups:

$12167\to 12$ and $167$

Unit's digit:

$\because$ 167 is ending in 7 and cube of a number ending in 3 ends in 7

$\therefore$ Unit's digit of the cube root $=3$

Ten's digit:

$\because 2^3=8,3^3=27$

and $8<12<27$

i.e $2^3<12<3^2$

$\therefore$ Ten's digit of the cube root is 2

$\therefore \sqrt[3]{3121367}=23$

(iv) Separating the given number (32768) into two groups:

$32768\to 32$ and $786$

Unit's digit:

768 will guess the unit's digit in the cube root.

$\because$ 768 ends in 8

$\therefore$ Unit's digit of the cube root $=2$

Ten's digit:

$\because 3^3=27,4^3=64$

and $27<32<64$

i.e $3^3<32<4^3$

$\therefore$ Ten's digit of the cube root is 3

$\therefore \sqrt[3]{332768}=32$