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how many zeros are at the end of (20!)2 when it is written in decimal form? fill in the blanks below to show how to use the result of part (b) to answer this question.
Therefore there are four zeros on the end of the number.



Answer :

varshamittal029

There are 8 zeroes at the end of [tex]20!^{2}[/tex]

Here, we are given an expression- [tex]20!^{2}[/tex]

To find the number of zeroes in any expression, we need to find the number of multiples of 10 in the expression.

10 is made up of 2 prime numbers, that are- 2 and 5

Thus, the number of multiples of 5 and 2 will give us the number of zeroes.

In 20!, the multiples of 5 will be- 5, 10, 15 and 20

⇒ there are total 4 multiples of 5 in 20!

Now, looking at the multiples of 2, we can see that there will definitely be more than 4 multiples, some of them are- 2, 4, 6, 8, 10 and so on

But since there are only 4 multiples of 5, there will be only 4 multiples of 10 and hence only 4 zeroes in the expansion of 20!

If we square 20!, the number of zeroes will also double and become 8

Thus, there are 8 zeroes at the end of [tex]20!^{2}[/tex]

Learn more about factorials here-

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