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Q.1 Find the cube root of each of the following numbers by prime factorisation method.

(i) 64

 

The detailed solution for the above-written question is as follows Prime factorization of 64 gives :         So its cube root is    = 4

Q.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?

Volume of cuboid is    To make it a cube need to make this a pefect cube number. So we need   cuboids  or      20 cuboids.  

Q.3  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

 

By prime factorization of given numbers :  (i) 81 :                     So given number needs to be divided by 3 to get a perfect cube. (ii) 128 :    .               So the given number needs to be divided by 2 to get a perfect cube. (iii) 135 :                   So the given number needs to be divided by 5 to get a perfect cube. (iv) 192 :                   So the given number needs to be...

Q.2 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

 

This can be found by knowing about the prime factors of the number. (i) 243 :     .                 So it must be multiplied by 3. (ii) 256 :                     So the given number must be multiplied by 2 to make it a perfect cube. (iii) 72 :                     So 72 must be multiplied by 3 to make it a perfect cube. (iv) 675 :                   So it should be multiplied by 5. (v) 100 :     ...

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

(v) 46656

We have 46656, by prime factorisation:        . Since prime numbers are in group of three. So the given number is a perfect cube.

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

(iv) 100

The detailed solution for the above-written question is as follows By prime factorization of 100 :      . Since prime numbers are not in pair of three so given number is not a perfect cube.

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

(iii) 1000

The detailed solution for the above written is as follows By prime factorization of 1000 we get :               .  So the given number is a perfect cube.

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

(ii) 128

We have 128.  By prime factorization we get,           Since the prime numbers are not in pairs of three, so the given number is not a perfect cube.

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

(i)  216

The detailed solution for the above-written question is as follows By prime factorization of 216 gives:            Since prime numbers are present in pairs of three, so the given number is a perfect cube.
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