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Find the square between \[75\] and \[90\].

Last updated date: 20th Jun 2024
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Hint: To find the square between the given numbers \[75\] and \[90\], we first check the range within which the square number is asked. The maximum range given is 90. So, as we know that square of 10 is 100. That means, the number we are looking for is less than 10. And the lower range given is 75, and as we know that square of the number 8 is 64. So between 8 and 10 we have the number 9 which has the square 81 which is between \[75\] and \[90\].

Complete step by step solution:
Square of a number is nothing but the product of the number by itself. For example - \[{{5}^{2}}=5\times 5=25\]
According to the question given, we have to find a number whose square is between \[75\] and \[90\],
We will try to list out the possible numbers that lie around the given range that is \[75\] and \[90\].
So starting with the lower range of the bracket given, we have 75,
Around 75, we have the 64 which is the square of the number 8. That is, \[{{8}^{2}}=8\times 8=64\]
Now, we know that the number having the square between \[75\] and \[90\] is greater than 8.
We now look at that maximum range in the given bracket, that is 90. We know that around 90 we have 100 which is the square of 10, that is, \[{{10}^{2}}=10\times 10=100\]
And now we know that the number we are looking for whose square lies in between \[75\] and \[90\] is less than 10.
So, the number lies between 8 and 10.
 \[{{8}^{2}}=8\times 8=64\]
\[{{9}^{2}}=9\times 9=81\]
\[{{10}^{2}}=10\times 10=100\]
So, the number is 9 which has its square between \[75\] and \[90\].
As \[{{9}^{2}}=9\times 9=81\] which lies \[75\] and \[90\].

Note: The square of a number should not be confused with the square root. Both are two different concepts. For example –
square of 8 is, \[{{8}^{2}}=8\times 8=64\]
And the square root of 8 is: \[\sqrt{8}=\sqrt{2\times 2\times 2}=2\sqrt{2}\]