What is the square root of $(4 x^{2} - 361) (4 x^{2} + 12 x + 9) (64 x^{2} - 5776)$ ?

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Solution

$\sqrt [(4 x^{2} - 361) (4 x^{2} + 12 x + 9) (64 x^{2} - 5776)] = \sqrt [(2 x - 19) (2 x + 19) (2 x + 3)^{2} (8 x - 76) (8 x + 76)]$

= $\sqrt [(2 x - 19) (2 x + 19) (2 x + 3)^{2} 4 (2 x - 19) 4 (2 x + 19)]$

= $\sqrt [4^{2} (2 x - 19) (2 x + 19) (2 x + 3)^{2} (2 x - 19) (2 x + 19)]$

= 4(2x–19)(2x + 19)(2x + 3)

= $4 (4 x^{2} - 361) (2 x + 3)$

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Question 1 (vii)
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