# Write the smallest four-digit number which is a perfect square.

A. $1000$

B. $1016$

C. $1024$

D. $1036$

Answer

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Hint: Find the square root of the smallest four-digit number. Use that information to get the answer.

We need to find the smallest four-digit number which is a perfect square. We know that 1000 is the smallest four-digit number. so, we’ll find the square root of that as follows:

Now, from the above process what we have understood is, ${(31)^2} < 1000$. It’s obvious that ${(32)^2} > 1000$. Let cross check once.$32 \times 32 = 1024 $. So, the smallest four-digit number is 1024.

Hence the correct option is C.

Note: For this kind of problem, it’s better to start the solution with the smallest/largest n-digit number then we can move further in the computation according to the given condition.

We need to find the smallest four-digit number which is a perfect square. We know that 1000 is the smallest four-digit number. so, we’ll find the square root of that as follows:

Now, from the above process what we have understood is, ${(31)^2} < 1000$. It’s obvious that ${(32)^2} > 1000$. Let cross check once.$32 \times 32 = 1024 $. So, the smallest four-digit number is 1024.

Hence the correct option is C.

Note: For this kind of problem, it’s better to start the solution with the smallest/largest n-digit number then we can move further in the computation according to the given condition.

Last updated date: 16th Sep 2023

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