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Find the least number by which 1323 must be multiplied so that the product is a perfect cube

Sagot :

bowmaian000

Answer:

Step-by-step explanation:

So, to solve this, lets just break down 1323.

Just looking at it, I am going to take a 3:

1323/3

=

441

So now we have:

3*441=1323

Can we break down 441 any more?

Yup, I can see that 3 goes into 450, 150 times and 441 is 9 less than 450, which means it 3 times less than 150 times, which is 147.

So now we have:

3*3*147=1323

Again, we can take something from 147.

7*20 is 140, and 147 is 7 more than that. So 7*21=147.

This further means:

3*3*7*21=1323

Now it probably isnt too difficult now.

21 can be broken down into 3*7.

So we can rewrite it as:

3*3*7*3*7=1323

And we can use exponents for the extra 3's and 7's we have, so we can simplfy it as:

3^3*7^2=1323

The perfect cube here is 3, since we cube 3(3^3), and then multiply it by 2 7s to make 1323.

The perfect square here is 7, since we square 7(7^2), and then multiply it by 3 3s.

So the PERFECT CUBE for your answer is 3.

The PERFECT SQUARE is 7.

Hope this helps!

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