Question

1. Find the smallest number by which 128 must be divided to obtain a perfect cube.
2. Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such
cuboids will he need to form a cube?
3. Find the cube root of 17576 through estimation.
4 You are told that 1.331 is a perfect cube. Can you guess without factorisation
what is its cube root? Similarly, guess the cube roots of 4913.12167,32768.​

Answer 1

Answer:

1) Hence the smallest number by which 128 should be divided to make a perfect cube is 2.

2) Given numbers = 5×2×5

Since, Factors of 5 and 2 both are not in group of three.

Therefore, the number must be multiplied by 2×5×2  = 20 to make it a perfect cube.

Hence he needs 20 cuboids.

3) Given number is 17576.

Split the number from right into the group of three digit numbers. We have 2 parts 17 and 576.the unit digit of 576 is 6.

Hence the unit digit of required cube root is 6.

Now, We have to estimate the cube root of 17.

It lies between 8 and 27 i.e cube of 2 and 3.   (2^3 = 8 and 3^3 = 27)

Take the units digit of the smallest number i.e 2.

So, The cube root of 17576 is 26.

4) 1331:

It lies between 10³ = 1000 and 20³ = 8000 and it’s last digit, 1, can’t be the cube but of 1, so:

Third root of 1331 = 11

4913:

It lies between 10³ = 1000 and 20³ = 8000 and it’s last digit, 3, can’t be the last digit of the cube of but 7, so:

Third root of 4913 = 17

12167:

It lies between 20³ = 8000 and 30³ = 27000 and it’s last digit, 7, can’t be the last digit of the cube of but 3, so:

Third root of 12167 = 23

32768:

32768 = 1024 * 32 = 2^10 * 2^5 = 2^15, so:

Third root of 2^15 = 2^5 = 32.

Step-by-step explanation: