Find the square root of the following:

(6x² + 5x –6) (6x²–x–2)(4x² + 8x + 3)

We factorize each of the above polynomials

6x² + 5x –6 = 6x² + 9x –4x –6

⇒ 6x² + 5x –6 = 3x(2x + 3)–2(2x + 3)

⇒ 6x² + 5x –6 = (3x–2)(2x + 3) …(i)

6x²–x–2 = 6x²–4x + 3x–2

⇒ 6x²–x–2 = 2x(3x–2) + 1(3x–2)

⇒ 6x²–x–2 = (2x + 1)(3x–2) …(ii)

4x² + 8x + 3 = 4x² + 6x + 2x + 3

⇒ 4x² + 8x + 3 = 2x(2x + 3) + 1(2x + 3)

⇒ 4x² + 8x + 3 = (2x + 1)(2x + 3) …(iii)

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

(6x² + 5x –6) (6x²–x–2)(4x² + 8x + 3) = (3x–2)²(2x + 3)²(2x + 1)²

Square Root = √ (3x–2)²(2x + 3)²(2x + 1)²

| (3x–2)(2x + 3)(2x + 1)|