# Find the least perfect square with four digits.

Last updated date: 18th Mar 2023

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Answer

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Hint: Here we go through by first finding the smallest four digit number then find out its roots if the root is not perfect then the next integer to that number is the perfect square root of the smallest four digit number and the square of that number is the least perfect square with four digits.

Complete step-by-step answer:

As we know the smallest four digit number is 1000, which is not a perfect square as we find the square root of 1000, i.e. $\sqrt {1000} \approx 31.622$ which does not give the perfect square root.

Hence the number after 31.622, i.e., 32 is the perfect square root of the smallest four digit number.

Which means 32's square will be a smallest four-digit perfect square.

$ \Rightarrow 32 \times 32 = 1024$

Hence, 1024 is the smallest four-digit number which is a perfect square.

Note: Whenever we face such type of question the key concept for solving the question is first find out the smallest digit number if it is not the perfect square of number then find outs roots and the next integer to that root gives the result i.e. the number whose square gives the least perfect square with four digits.

Complete step-by-step answer:

As we know the smallest four digit number is 1000, which is not a perfect square as we find the square root of 1000, i.e. $\sqrt {1000} \approx 31.622$ which does not give the perfect square root.

Hence the number after 31.622, i.e., 32 is the perfect square root of the smallest four digit number.

Which means 32's square will be a smallest four-digit perfect square.

$ \Rightarrow 32 \times 32 = 1024$

Hence, 1024 is the smallest four-digit number which is a perfect square.

Note: Whenever we face such type of question the key concept for solving the question is first find out the smallest digit number if it is not the perfect square of number then find outs roots and the next integer to that root gives the result i.e. the number whose square gives the least perfect square with four digits.

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