Find the cube root of the following numbers through estimation’?(i)

Find the cube root of the following numbers through estimation’?(i) 3375 (ii) 5832

Answer»

(i) 3375

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

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.

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