Find the cube roots of each of the following integers:(i)-125 (ii)

1.	Find the cube roots of each of the following integers:(i)-125 (ii) -5832(iii)-2744000
Answer» (i) -125 -125 = ∛-125 = -∛125 = ∛ (5×5×5) = -5 (ii) -5832 -5832 = ∛-5832 = -∛5832 Where, unit digit of 5832 = 2 Unit digit in the cube root of 5832 will be 8 After striking out the units, tens and hundreds digits of 5832, Now we left with 5 only. As we know that 1 is the Largest number whose cube is less than or equal to 5. So, the tens digit of the cube root of 5832 is 1. ∛-5832 = -∛5832 = -18 (iii) -2744000 ∛-2744000 = -∛2744000 2744000 = 2×2×2×2×2×2×5×5×5×7×7×7 2744000 = (2×2×2) × (2×2×2) × (5×5×5) × (7×7×7) = 2×2×5×7 = 140 ∴ ∛-2744000 = -∛2744000 = -140

Find the cube roots of each of the following integers:(i)-125 (ii) -5832(iii)-2744000

Answer»

(i) -125

-125 = ∛-125

= -∛125

= ∛ (5×5×5)

= -5

(ii) -5832

-5832 = ∛-5832

= -∛5832

Where, unit digit of 5832 = 2

Unit digit in the cube root of 5832 will be 8

After striking out the units, tens and hundreds digits of 5832,

Now we left with 5 only.

As we know that 1 is the Largest number whose cube is less than or equal to 5.

So, the tens digit of the cube root of 5832 is 1.

∛-5832 = -∛5832

= -18

(iii) -2744000

∛-2744000 = -∛2744000

2744000 = 2×2×2×2×2×2×5×5×5×7×7×7

2744000 = (2×2×2) × (2×2×2) × (5×5×5) × (7×7×7)

= 2×2×5×7

= 140

∴ ∛-2744000 = -∛2744000

= -140