Question

Find the cube root of following number through estimation.
1)10648
2)15625
3)110592
4)91125

Answer 1

1) 22
2) 25
3) 48
4) 48

Answer 2

Given :  (i) 10648 (ii) 15625 (iii) 110592  (iv)  91125​

To find : cube root through estimation.

Solution:

10648

end with 8

hence unit digit of cube root should be 2

27000 > 10648   > 8000

=> 30000 > ∛10648  >  20

greater than 20  and less than 30 ending with digit 2

so ∛10648  = 22

15625

end with 5

hence unit digit of cube root should be 5

27000 > 15625  > 8000

=>   30 > ∛15625 >  20

greater than 20  and less than 30 ending with digit 5

∛15625  = 25

∛110592  = 48    

110592  end with 2

hence unit digit of cube root should be 8

125000 > 110592 > 64000

50 > ∛110592 > 40

greater than 40  and less than 50 ending with digit 8

∛110592  = 48    

110592  end with 5

hence unit digit of cube root should be 5

125000 > 91125  > 64000

50 > ∛91125  > 40

greater than 40  and less than 50 ending with digit 5

∛91125  = 45

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