Find the square root of the following:

(x² – 25)( x² + 8x + 15)( x² –2x–15)

We factorize each of the above polynomials

x² – 25 = x² – 5²

Since it is in the form of a²–b² = (a–b)(a + b)

⇒ x² – 25 = (x–5)(x + 5) …(i)

x² + 8x + 15 = x² + 5x + 3x + 15

⇒ x² + 8x + 15 = x(x + 5) + 3(x + 5)

⇒ x² + 8x + 15 = (x + 3)(x + 5) …(ii)

x² –2x–15 = x² –5x + 3x–15

⇒ x² –2x–15 = x(x–5) + 3(x–5)

⇒ x² –2x–15 = (x + 3)(x–5) … (iii)

Combining (i), (ii) & (iii) we get

(x² – 25)( x² + 8x + 15)( x² –2x–15) = = (x–5)²(x + 5)²(x + 3)²

Square Root = √[(x–5)²(x + 5)²(x + 3)²]

|(x–5)(x + 5)(x + 3)|