# Find the least number which must be subtracted from each of the following numbers so as to get a perfect square . Also find the square root of the perfect square so obtained

(i)402, (ii) 1989, (iii) 3250, (iv)825 (v) 4000

A. Least number which must be subtracted : (i)2, (ii)22, (iii)1,(iv)21,(v)52

Square root of the perfect square

(i)20 (ii)34 (iii)55 (iv)26 (v)67

B. Least number which must be subtracted : (i)2, (ii)53, (iii)1,(iv)41,(v)31

Square root of the perfect square

(i)20 (ii)44 (iii)57 (iv)28 (v)63

C. Least number which must be subtracted : (i)6, (ii)22, (iii)50,(iv)31,(v)40

Square root of the perfect square

(i)19 (ii)41 (iii)49 (iv)27 (v)65

D. Least number which must be subtracted : (i)8, (ii)41, (iii)12,(iv)56,(v)4

Square root of the perfect square

(i)19 (ii)22 (iii)37 (iv)26 (v)61

Answer

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Hint: Find the nearest square to the given numbers and then find the difference between them and solve it and then find the square root.

Complete step-by-step answer:

The given numbers are 402,1989,3250,825,4000

(i) Let us consider the first number 402

402 is not a perfect square

The nearest perfect square is 400

So, 402-2=400

So, the least number which must be subtracted is 2

The square root of 400= 20

(ii)Let us consider the second number 1989

1989 is not a perfect square

The nearest perfect square is 1936

So, 1989-1936=53

So, the least number which must be subtracted is 53

Now, the square root of 1936 = 44

(iii) Let us consider the third number 3250

It is not a perfect square

The nearest perfect square is 3249

So, 3250-1=3249

So, the least number which has to be subtracted is 1

The square root of 3249=57

(iv) Let us consider the fourth number 825

It is not a perfect square

The nearest perfect square is 784

So, 825-784=41

So, the least number which has to be subtracted is 41

The square root of 784 is 28

(v) Let us consider the fifth number 4000

It is not a perfect square

The nearest perfect square is 3969

So, 4000-3969=31

So, the least number which has to be subtracted is 31

The square root of 3969 is 63.

So, from this, we can say

Least number which must be subtracted are (i)2, (ii)53, (iii)1,(iv)41,(v)31 respectively

Square root of the perfect square are

(i)20 (ii)44 (iii)57 (iv)28 (v)63 respectively

So, option B is the correct answer to this question

Note: Whenever solving these type of problems , find out the nearest perfect square by inspection and from that find out the difference between the two numbers and then find out the square root of the perfect square.

Complete step-by-step answer:

The given numbers are 402,1989,3250,825,4000

(i) Let us consider the first number 402

402 is not a perfect square

The nearest perfect square is 400

So, 402-2=400

So, the least number which must be subtracted is 2

The square root of 400= 20

(ii)Let us consider the second number 1989

1989 is not a perfect square

The nearest perfect square is 1936

So, 1989-1936=53

So, the least number which must be subtracted is 53

Now, the square root of 1936 = 44

(iii) Let us consider the third number 3250

It is not a perfect square

The nearest perfect square is 3249

So, 3250-1=3249

So, the least number which has to be subtracted is 1

The square root of 3249=57

(iv) Let us consider the fourth number 825

It is not a perfect square

The nearest perfect square is 784

So, 825-784=41

So, the least number which has to be subtracted is 41

The square root of 784 is 28

(v) Let us consider the fifth number 4000

It is not a perfect square

The nearest perfect square is 3969

So, 4000-3969=31

So, the least number which has to be subtracted is 31

The square root of 3969 is 63.

So, from this, we can say

Least number which must be subtracted are (i)2, (ii)53, (iii)1,(iv)41,(v)31 respectively

Square root of the perfect square are

(i)20 (ii)44 (iii)57 (iv)28 (v)63 respectively

So, option B is the correct answer to this question

Note: Whenever solving these type of problems , find out the nearest perfect square by inspection and from that find out the difference between the two numbers and then find out the square root of the perfect square.

Last updated date: 16th Sep 2023

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