Find the least perfect square with four digits.
Answer
380.7k+ views
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.
Recently Updated Pages
Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What is pollution? How many types of pollution? Define it

Give 10 examples for herbs , shrubs , climbers , creepers

Which planet is known as the red planet aMercury bMars class 6 social science CBSE

Which state has the longest coastline in India A Tamil class 10 social science CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE
