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Question

# Which of the following operations can convert the expression (x2+8x√3) into a perfect square?

A
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B
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C
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D
Subtraction of 8x3
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Solution

## The correct option is B Addition of (4√3)2.To make x2+8x√3a perfect square, divide the co-efficient of x by 2 and the add the square of the result to x2+8x√3to convert it into a perfect square. ∴Adding (8√3÷2)2=(4√3)2 to x2+8x√3, we have, x2+8x√3+(4√3)2=x2+2(x)(4√3)+(4√3)2=(x+4√3)2, a perfect square (Using the identity, (a+b)2=a2+2ab+b2)

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