Find the least number which must be added from each of the following so as to get a perfect square. Also find the square root of the perfect square so obtained.
(i)525 (ii) 1750 (iii) 252 (iv) 1825 (v) 6412
Last updated date: 17th Mar 2023
•
Total views: 309.3k
•
Views today: 4.91k
Answer
309.3k+ views
Hint: Find the greatest perfect square for a number and subtract from it.
The approach to find the least number that should be added to the given numbers in order to make them perfect square is that we need to find a greater perfect number which is closest to the given number.
(i) 525
The closest perfect square number to 525 is 576 hence difference between two of them is $576 - 525 = 51$
Thus 51 must be added to 525 make it a perfect square thus $\sqrt {576} = 24$
(ii) 1750
The closest perfect square number to 1750 is 1764 hence difference between two of them is
$1764 - 1750 = 14$
Thus 14 must be added to 1750 make it a perfect square thus $\sqrt {1764} = 42$
(iii) 252
The closest perfect square number to 252 is 256 hence difference between two of them is $256 - 252 = 4$
Thus 4 must be added to 252 make it a perfect square thus $\sqrt {256} = 16$
(iv) 1825
The closest perfect square number to 1825 is 1849 hence difference between two of them is $1849 - 1825 = 24$
Thus 24 must be added to 1825 make it a perfect square thus $\sqrt {1849} = 43$
(v) 6412
The closest perfect square number to 6412 is 6561 hence difference between two of them is $6561 - 6412 = 149$
Thus 149 must be added to 6412 make it a perfect square thus $\sqrt {6561} = 81$
Note: Whenever we need to solve such problem statements we simply need to find the closest perfect square to that given number thus eventually their difference will give us the number that should be added in order to make the perfect square.
The approach to find the least number that should be added to the given numbers in order to make them perfect square is that we need to find a greater perfect number which is closest to the given number.
(i) 525
The closest perfect square number to 525 is 576 hence difference between two of them is $576 - 525 = 51$
Thus 51 must be added to 525 make it a perfect square thus $\sqrt {576} = 24$
(ii) 1750
The closest perfect square number to 1750 is 1764 hence difference between two of them is
$1764 - 1750 = 14$
Thus 14 must be added to 1750 make it a perfect square thus $\sqrt {1764} = 42$
(iii) 252
The closest perfect square number to 252 is 256 hence difference between two of them is $256 - 252 = 4$
Thus 4 must be added to 252 make it a perfect square thus $\sqrt {256} = 16$
(iv) 1825
The closest perfect square number to 1825 is 1849 hence difference between two of them is $1849 - 1825 = 24$
Thus 24 must be added to 1825 make it a perfect square thus $\sqrt {1849} = 43$
(v) 6412
The closest perfect square number to 6412 is 6561 hence difference between two of them is $6561 - 6412 = 149$
Thus 149 must be added to 6412 make it a perfect square thus $\sqrt {6561} = 81$
Note: Whenever we need to solve such problem statements we simply need to find the closest perfect square to that given number thus eventually their difference will give us the number that should be added in order to make the perfect square.
Recently Updated Pages
If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts
What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

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

Name the Largest and the Smallest Cell in the Human Body ?
