Factorisation method to find the square root of $(x^{2} - 12 x + 35)^{4}$ .

∣ ∣ (x - 7)^{2} (x - 5)^{2} ∣ ∣

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∣ ∣ (x - 7) (x - 5)^{2} ∣ ∣

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∣ ∣ (x - 7)^{2} (x - 5) ∣ ∣

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(x - 7)^{2} (x - 5)^{2}

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Solution

The correct option is A $∣ ∣ (x - 7)^{2} (x - 5)^{2} ∣ ∣$
$\sqrt{(x^{2} - 12 x + 35)^{4}}$
Factor of $x^{2} - 12 x + 35 = (x - 7) (x - 5)$
So, $\sqrt{(x^{2} - 12 x + 35)^{4}} = \sqrt{((x - 7)^{2} (x - 5)^{2})^{2}}$
$=$ $∣ ∣ (x - 7)^{2} (x - 5)^{2} ∣ ∣$

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