(i) We know that for any two integers a and b,

So from this property, we have:

(ii) By Applying a and b, , we have

To find out cube root by using units digit:

Let’s take the number 1728.

So,

Unit digit = 8

The unit digit in the cube root of 1728 = 2

After striking out the units, tens and hundreds digits of the given number, we are left with the 1.

As we know 1 is the largest number whose cube is less than or equals to 1.

So,

The tens digit of the cube root of 1728 = 1

Prime factors of 216 = 2×2×2×3×3×3

On grouping the factors in triples of equal factor,

We have,

216 = {2×2×2}×{3×3×3}

Taking one factor from each group we get,

So,

(iii) By Applying a and b propertise, , we have

To find out cube root by using units digit:

Let’s take the number 2744.

So,

Unit digit = 4

The unit digit in the cube root of 2744= 4

After striking out the units, tens and hundreds digits of the given number, we are left with the 2.

As we know 1 is the largest number whose cube is less than or equals to 2.

So,

The tens digit of the cube root of 2744 = 1

Prime factors of 216 = 2×2×2×3×3×3

On grouping the factors in triples of equal factor,

We have,

216 = {2×2×2}×{3×3×3}

Taking one factor from each group we get,

So,

(iv) By Applying a and b propertise,, we have

To find out cube root by using units digit:

Let’s take the number 15625.

So,

Unit digit = 5

The unit digit in the cube root of 15625 = 5

After striking out the units, tens and hundreds digits of the given number, we are left with the 15.

As we know 2 is the largest number whose cube is less than or equals to 15(2³<15<3³).

So,

The tens digit of the cube root of 15625 = 2

Also

As we know 9×9×9 = 729

Thus,