Question

Find the least $8$ digit number which is a perfect square.

Answer 1

Hint:Here, we will first write down the smallest eight digit number. After that we will find the square root of the given number and then we will check whether the given number is a perfect square or not by calculating its square. Since we know that the smallest eight digit number is $10000000$.

Complete step by step answer:
We have to find the least eight digit number which is a perfect square. The smallest eight digit number is $10000000$. Now we have to find the square root of this number to determine the perfect square, so we can write this as:
$ \Rightarrow \sqrt {10000000} = \sqrt {10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10} $
Now the numbers that are in pairs can be removed from the under square root as they are perfect squares, so it can be written as:
$ \Rightarrow 10 \times 10 \times 10 \times \sqrt {10} $

On multiplying the numbers, we have:
$1000\sqrt {10} $
Now we will substitute the value$\sqrt {10} = 3.162$ (approx.) on the expression and it gives:$1000 \times 3.162$
It gives the value $3163$(approx.)
Since we get the number in decimal, so we will multiply the above number by itself, therefore we have: $3163 \times 3163$
It gives us the number: $10004569$

Hence the least $8$ digit number which is a perfect square is $10004569$.

Note:We should note that a perfect square can be obtained when an integer is multiplied by itself. An integer is a number which is neither a decimal or fraction. Therefore this is why we have converted the decimal to its rounding off figure to get the answer. We should note that if we find the integer small then w e will not get the perfect square of eight digit, it can be less than an eight digit number.