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in Cubes And Cube Roots by (41.5k points)
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Find the cube root of the following numbers through estimation’? 

(i) 512 

(ii) 2197 

1 Answer

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Best answer

i) 512

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

i.e., \(\overline{512}\) First group is 512 

Step 2: First group i.e. 512 will give us the units digit of the cube root. As 512 ends with 2, then its cube root ends with 8 (2 x 2 x 2) So the units place of the cube root will be 8.

Step 3: Now take the second group i.e. 0.Which is 03 < 1 < 23

So the least number is ‘0′. 

∴ Tens digit of a cube root of a number be 0. 

∴ \(\sqrt[3]{512}\) = 08 = 8

(ii) 2197 

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

2 197
second first
group group

Step 2: First group i.e., 197 will give us the units digit of the cube root. 

As 197 ends with 7, its cube root ends with 3. ‘

 [∵ 3 x 3 x 3 = 27] 

∴ Its units digit is 7.

Step 3: Now take the second group i.e.,2 

We know that i3 < 2 < 2 

∴ The least number be 1. 

∴ The required number is 13.

∴ \(\sqrt[3]{2197}\) = \(\sqrt[3]{13\,\times\,13\,\times13}\) = \(\sqrt[3]{13}{^3}\) = 13

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