Find the square root of the following:

(2x² –5x + 2) (3x²–5x–2) (6x² – x –1)

We factorize each of the above polynomials

2x² –5x + 2 = 2x²–4x–x + 2

⇒ 2x² –5x + 2 = 2x(x–2)–1(x–2)

⇒ 2x² –5x + 2 = (2x–1)(x–2) …(i)

3x²–5x–2 = 3x²–6x + x–2

⇒ 3x²–5x–2 = 3x(x–2) + 1(x–2)

⇒ 3x²–5x–2 = (3x + 1)(x–2) …(ii)

6x² – x –1 = 6x²– 3x + 2x–1

⇒ 6x² – x –1 = 3x(2x–1) + 1(2x–1)

⇒ 6x² – x –1 = (3x + 1)(2x–1) …(iii)

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

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

Square Root = √(2x–1)²(x–2)²(3x + 1)²

|(2x–1)(x–2)(3x + 1)|