Mathematics

Grade-8

Easy

Question

Which is the greatest three-digit perfect square?

999
961
962
970

hint Hint:

A square in mathematics is created by multiplying a whole number by itself. The result of a number 3 multiplied by itself, for instance, is 9. 9 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 greatest three-digit perfect square.

The correct answer is: 961

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: 961
$square root of 961 equals square root of 31 cross times 31 end root square root of 961 equals 31$
So this number is a perfect square.
Number 2: 962
$square root of 962 equals square root of 2 cross times 13 cross times 37 end root$
So this number is not a perfect square.
Number 3: 999
$square root of 999 equals square root of 3 cross times 3 cross times 3 cross times 37 end root square root of 1024 equals 3 cross times square root of 3 cross times 37 end root$
So this number is not a perfect square.
Number 4: 970
$square root of 970 equals square root of 10 cross times 97 end root$
So this number is not a perfect square.
So out of all the four numbers given, we have 961 as 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.

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Which is the greatest three-digit perfect square?

999961962970

The correct answer is: 961

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