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- Cube Roots : Solution of NCERT Exercise 7.1

**Exercise 1**

**1. Which of the following numbers are not perfect cubes?**

**(i) 216 **

**Answer:** 216 = 2 x 2 x 2 x 27

= 2 x 2 x 2 x 3 x 3 x 3

As number of 2s and 3s is 3 in the factorization so it is a perfect cube.

**(ii) 128 **

**Answer:** 128 = 2 x 2 x 2 x 2 x 2 x 2 x 2

Number of 2s is 7 and 7 is not divisible by three so 128 is not a perfect cube

**(iii) 1000 **

**Answer:** 1000 = 2 x 2 x 2 x 5 x 5 x 5

Number of 2s and 5s is 3 each so 1000 is a perfect cube.

**(iv) 100 **

**Answer:** 100 = 2 x 2 x 5 x 5

Number of 2s and 5s is 2 each and not 3 so 100 is not a perfect cube.

**(v) 46656**

**Answer:** 46656 = 2 x 2 x 2 x 5832

= 2 x 2 x 2 x 2 x 2 x 2 x 729

= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3

Number of 2s and 3s is 6 each and 6 is divisible by 3 so 46656 is a perfect cube

**2. Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.**

**(i) 243 **

**Answer:** 243 = 3 x 3 x 3 x 3 x 3

Number of 3s is 5, so we need to another 3 in the factorization to make 243 a perfect cube. 243 multiplied by 3 will be a perfect cube.

**(ii) 256 **

**Answer:** 256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Number of 2s is 8 so 256 needs to be multiplied by 2 to become a perfect cube.

**(iii) 72 **

**Answer:** 72 = 2 x 2 x 2 x 3 x 3

Number of 2s is 3 and that of 3s is 2, so 72 needs to be multiplied by 3 to become a perfect cube.

**(iv) 675**

**Answer:** 675 = 5 x 5 x 27 = 5 x 5 x 3 x 3 x 3

675 needs to be multiplied by 5 to become a perfect cube.

**(v) 100**

**Answer:** 100 = 10 x 10

100 needs to be multiplied by 10 to become a perfect cube.

**3. Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube.**

**(i) 81 **

**Answer:** 81 = 3 x 3 x 3 x 3

81 needs to be divided by 3 to become a perfect cube.

**(ii) 128 **

**Answer:** 128 = 2 x 2 x 2 x 2 x 2 x 2 x 2

128 needs to be divided by 2 to become a perfect cube.

**(iii) 135 **

**Answer:** 135 = 5 x 3 x 3 x 3

135 needs to be divide by 5 to become a perfect cube.

**(iv) 192**

**Answer:** 192 = 2 x 2 x 2 x 2 x 2 x 2 x 3

192 needs to be divided by 3 to become a perfect cube.

**(v) 704**

**Answer:** 704 = 2 x 2 x 2 x 2 x 2 x 2 x 11

704 needs to be divided by 11 to become a perfect cube.

**4. 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?**

**Answer:** To find the answer we need to calculate the LCM of 5 and 2. The cube with each sides measuring equal to the LCM will give the dimensions of required cube.

LCM of 5 and 2 = 10

Volume of cuboid = 5 x 5 x 2 cubic cms

Volume of bigger cube=103=1000 cubic cms

Number of cuboids required to make the bigger cube =

Cube And Cube Roots will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.