Which is the smallest 4-digit perfect square?

1024
1025
1000
1016

hint Hint:

A square in mathematics is created by multiplying a whole number by itself. The result of a number 2 multiplied by itself, for instance, is 4. 4 is referred to as a perfect square in this instance.
When two equal integers are multiplied by one another, a perfect square is produced.
Here we have given 4 numbers where we have to determine the smallest 4-digit perfect square.

The correct answer is: 1024

Now we know that when two equal integers are multiplied by one another, a perfect square is produced. So we will start finding the square root of the given numbers one by one and then finalize which one is the smallest perfect square number.
Number 1: 1016
$square root of 1016 equals square root of 127 cross times 2 cross times 2 cross times 2 end root square root of 1016 equals 2 cross times square root of 127 cross times 2 end root$
So this number is not a perfect square.
Number 2: 1025
$square root of 1025 equals square root of 5 cross times 5 cross times 41 end root square root of 1016 equals 5 cross times square root of 41$
So this number is not a perfect square.
Number 3: 1024
$square root of 1024 equals square root of 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 end root square root of 1024 equals 2 cross times 2 cross times 2 cross times 2 cross times 2 square root of 1024 equals 32$
So this number is a perfect square.
Number 4: 1000
$square root of 1000 equals square root of 5 cross times 5 cross times 5 cross times 2 cross times 2 cross times 2 end root square root of 1000 equals 5 cross times 2 cross times square root of 10 square root of 1000 equals 10 cross times square root of 10$
So this number is not a perfect square.
So out of all the four numbers given, we have 1024 as the smallest 4-digit perfect square.

In this question we were given 4 numbers out of which we have to find the smallest 4-digit perfect square. We used the concept of perfect square and found the factors of all the numbers out of which 1024 was found to be the smallest 4-digit perfect square.

Which is the greatest three-digit perfect square?

In this question we were given 4 numbers out of which we have to find the greatest three-digit perfect square. We used the concept of perfect square and found the factors of all the numbers out of which 961 was found to be the greatest three-digit perfect square.