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Find the square root of the following number: .

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answer is C.

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Detailed Solution

Concept: The given number is

.
As we know that the square root of

will be of the form

.
So, consider

is the square root of the given number.

Now we will find the value of x and y by squaring both sides of the equation (1), we get

By applying

identity, we get
Question Image

Thus, the root part and the other parts of the above equation will also be equal if the LHS and RHS are equal. Consequently we get
Question Image

By squaring equation 4, we get

Now we will find the value of x and y by solving equations (3) and (5).
From equation 5, we have

Replace x in equation 3 with its value.
Question Image

Further we will put the value of y in equation 6, we get
When

When

So, the value of x and y are

By putting the value of x and y in

, we get

Hence, the correct answer is option (3).

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