5. What is $\sqrt{123454321}$ ?
A 1111111
B 111111
C 11111
D 1111
E 111
SolUTION
C

Note: You could not be expected to be able to calculate the value of $\sqrt{123454321}$ without the use of a calculator. So you need to find some other way to select the correct option. We use a method based on the size of the number 123454321 .

We have
$$
10^{8}<123454321<10^{10} .
$$

Therefore
$$
\sqrt{10^{8}}<\sqrt{123454321}<\sqrt{10^{10}},
$$
that is,
$$
10^{4}<\sqrt{123454321}<10^{5} .
$$

The correct option is therefore the only one that is between $10^{4}$ and $10^{5}$. Therefore, of the given options, it is 11111 that equals $\sqrt{123454321}$.

For INVESTIGATION
5.1 The answer given above assumes that one of the given options is correct. Verify that $11111=\sqrt{123454321}$ by checking that $11111^{2}=123454321$.