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Find the square root of given :
21440
(a) 1210(b) 116(c) 1110(d) 102

Answer
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Hint – In this question let the square root of 21440 be of the form ab that is ab=21440, then apply proper algebraic identities to get the value of a and b. Substitute them back to get the right answer.

Complete step-by-step answer:
Given equation
21440
Square root of given equation is
21440
There are two terms in the given equation therefore in the square root of this it also has two terms.
So, let ab=21440
Squaring both sides
(ab)2=(21440)2
Now, as we know that (ac)2=a2+c22ac so use this property in above equation we have,
a+b2ab=21440
So, on comparing
a+b=21...................(1), 2ab=440 
So on squaring both sides we have,
(a+b)2=(21)2 = 441............(2), 4ab=440.................(3)
Now it is a known fact that that (ab)2=(a+b)24ab
So from equation (2) and (3) we have,
(ab)2=441440=1
Now take square root on both sides we have,
(ab)=1=1…………………. (4)
From add equation (1) and (4) we have
a+b+ab=21+1
2a=22
a=11
Now from equation (1)
b=21a=2111=10
So the required square root is 1110
So, this is the required square root.
Hence option (C) is the correct answer.

Note – There is a specific format for solving problems of this kind. Which is to assume the square root in terms of some variables. Since the direct square root could only be found for numbers which are perfect square thus there is no direct way for finding the square root of numbers mentioned in this problem. The basic definition of square root is a number which produces a specified quantity when the number is multiplied to itself twice.
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