Question

Find the cube root of the following numbers through estimation’?

(i) 3375 

(ii) 5832

Answer 1

(i) 3375 

Step 1: Start making groups of three digits starting from the unit place. i.e.;

3	375
second	first
Group	Group

Step 2: First group is 375. Its units digit is 5. 

∴ The cube root is also ends with 5. 

∴ The units place of the cube root will be 5.

Step 3: Now take the second group,

 i.e., 3 we know that 1³ < 3³ <2³ 

∴ The least number is 1. 

∴ The tens digit of a cube root will be 1. 

∴ The required number = 15

 ∴ \(\sqrt[3]{3375}\) = \(\sqrt[3]{15\,\times\,15\,\times15}\) = \(\sqrt[3]{15}{^3}\) = 15

(ii) 5832 

Step 1: Start making groups of three digits starting from the unit place.

5	832
second	first
group	group

Step 2: The units digit of 832 is 2. 

∴ The cube root of the number ends with units digit 8. 

[∵ 8 x 8 x 8 = 512]

Step 3: In the second group i.e., 5 lie between 1 and 6

 i.e., 1³ < 5 < 2³ 

∴ The tens digit of a number will bel. 

∴ The required number is 18.

∴ \(\sqrt[3]{5832}\) = \(\sqrt[3]{18\,\times\,18\,\times18}\) = \(\sqrt[3]{18}{^3}\) = 18