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Which of the following numbers are not perfect cubes?

(i) 216

.(ii) 128

(iii) 1000

(iv) 100

(v) 46656

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

Therefore

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

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

Therefore

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

= 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

Therefore

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

(i) 243

(ii) 256

(iii) 72

(iv) 675

(v) 100

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.

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

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

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

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

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

(i) 81

(ii) 128

(iii) 135

(iv) 192

(v) 704

So we have 4 3’s,Therefore

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

So we have 7 2’s,Therefore

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

So we have 1 5’s and 3 3’s Therefore

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

iv) 192 = 2 x 2 x 2 x 2 x 2 x 2 x 3

So we have 6 2’s and 1 3’s Therefore

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

So we have 6 2’s and 1 11’s Therefore

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

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?

If we multiply this expression by 2×2×5, The it become perfect cube.

Now Volume of cube is given by

=a

So that means we need 2×2×5=20 cuboid to make the cube

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