Calculate the square root of the polynomial using factorisation method: $\frac{x^{2} + 2 x + 1}{(x + 1)^{4}}$

\frac{1}{(x + 1)^{2}}

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\frac{1}{x + 1}

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\frac{2}{x + 1}

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\frac{1}{x - 1}

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Solution

The correct option is B $\frac{1}{x + 1}$
$\sqrt{\frac{x^{2} + 2 x + 1}{(x + 1)^{4}}}$
Factor of $x^{2} + 2 x + 1 = (x + 1)^{2}$
$=$ $\sqrt{\frac{(x + 1)^{2}}{(x + 1)^{4}}}$
$=$ $\sqrt{\frac{1}{(x + 1)^{2}}}$
$=$ $\frac{1}{x + 1}$

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