Question

the least number that should be multiplied to 4320 to make it a perfect cube

Answer 1

Hello Dear!!!!

Here's your answer...

The given number is 4320

first,we have to do prime factorization

4320 = 2*2*2*2*2*3*3*3*5

4320 = 2^3 * 2^2 * 3^3 * 5

Here,

The power of 3 is 3

but the power of remaining 2 and 5 is not 3

The power of one 2 is 3....but the power of other 2 is 2

so...to become a perfect cube...the power should be 3

so...it should it multiplied with 2

The power of 5 is 1

It should be 3

so...we have to multiply two 5's

so...5*5 is 25

so...totally..

we have to multiply one 2 and two 5's

2*5*5

50

50 should be multiplied with 4320 to become perfect cube....

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HOPE THIS HELPS YOU....

Answer 2

Hey Mate !

Here is your solution :

Let's know some terms.

What is a perfect cube ?

If a number is multiplied by itself thrice,then the number that is formed is known as a Perfect Cube.

Prime Factorization of 4320.

4320 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5

4320 = 2³ × 2² × 3³ × 5

Here,

Once, 2 is already multiplied by itself thrice.

3 is also multiplied by itself thrice.

But ,

One 2 is only multiplied itseld by twice, so we have to multiply it once by itself ( 2 ).

And , 5 is also multipled by itself once,so we have to multiply 5 by itself twice ( 5² ).

Now,

=> 2³ × 2³ × 3³ × 5³ = ( 2 × 2 × 3 × 5 )³

= ( 60 )³ = 60 × 60 × 60

Therefore, the required answer is ( 2 × 5² = 50 ).

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Hope it helps !! ^_^