Question

Q. 3. You are told that 1,331 is a perfect
cube. Can you guess without factorisation
what is its cube root? Similarly, guess the
cube roots of 4913, 12167, 32768.)
​

Answer 1

SOLUTION

For 1331:

Units digit of the cube root of 1331 is 1 as units digit of the cube root of numbers ending in 1 is 1. After striking three digits from the right of 1331, we get the number 1. Since 1^3 = 1, so the tens digit of the cube root of given number is 1.

Therefore,

$3 \sqrt{1331} = 11$

For 4913:

Units digit of the cube root of 4913 is 7 as units digit of cube root of numbers ending in 3 is 7. After striking three digits from the right of 4913, we get the number 4. As 1^3= 1 & 2^3= 8, so 1^3<4<2^3. Therefore, the tens digit of cube root of 4913 is 1.

Therefore,

$3 \sqrt{4913} = 17$

For 12167:

Unit's digit of the cube root of 12167 is 3 as units digit of cube root of numbers ending in 7 is 3. After striking three digits from the right of 12167,we get the number 12.As 2^3= 8 & 3^3= 27, so 2^3<12<3^3. So, the tens digit of the cube root of 12167 is 2.

Therefore,

$3 \sqrt{12167} = 23$

For 32768:

Units digit of the cube root of 32768 is 2 as units digit of cube root of numbers ending in 8 is 2. After striking three digits from the right of 32768, we get the number 32. As 3^3= 27 & 4^3= 64, so 3^3<32< 4^3. So, the tens digit of the cube root of 32768 is 3.

Therefore,

$3 \sqrt{32768} = 32$

hope it helps ☺️

Answer 2

hey Nancy..

here is your answer..

refer to the aatachment