Question

3. Find the least number by which 750 should be multiplied, so that it
becomes a perfect cube. Also, find the least number by which 750 should
be divided so that it becomes a perfect cube.

Answer 1

Answer:

36

Step-by-step explanation:

prime Factorization of 750: (2*3*5*5*5*)

= (2*2)*(3*3)

= 36

I hope it is useful to you

Answer 2

The least number that should be multiplied to 750 is 6 to get 125

The least number by which 750 should be divided is 36 to get 27000

Given:

Number 750

To find:

Find the least number by which 750 should be divided so that it becomes a perfect cube.

Solution:

A perfect cube number:

• A perfect cube number is a number which is obtained by multiplying a same number three times or a number which can be written in the form of a³  
• Example:  

           8 is a cube number, since 8 = 2³

            64 is cube number, sine 64 = 4³

Given number 750

Write given number as product of prime factors

⇒ 750 = 2 × 3 × 5 × 5 × 5    

Now group out the factors as triplets

⇒  5³ × 2 × 3  

Here, 2 and 3 cannot be written as triplets

So get perfect cube from 750, divide 750 by (2×3)  

⇒ 750/6 = 125

And also multiply 750 to get a perfect cube 2²3²

⇒ 750 × 2²3²  

⇒ 750 × 36 = 27000  

The least number that should be multiplied to 750 is 6 to get 125

The least number by which 750 should be divided is 36 to get 27000

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