
Example: Find the square root of (x^{2} + 7x + 12)(x^{2} + 10x + 24)(x^{2} + 9x + 18). Solution: Take the factors, x^{2} + 7x + 12 = x^{2} + 4x + 3x + 12 = x(x + 4) + 3(x + 4) = (x + 3)(x + 4) x^{2} + 10x + 24 = x^{2} + 4x + 6x + 24 = x(x + 4) + 6(x + 4) = (x + 4)(x + 6) x^{2} + 9x + 18 = x^{2} + 6x + 3x + 18 = x(x + 6) + 3(x + 6) = (x + 3)(x + 6) Therefore, (x^{2} + 7x + 12)(x^{2} + 10x + 24)(x^{2} + 9x + 18) = (x + 3)(x + 4)(x + 4)(x + 6)(x + 3)(x + 6) = (x + 3)^{2} (x + 4)^{2} (x + 6)^{2} The square root is (x + 3)(x + 4)(x + 6) Directions: Solve the following problems using above method. Also write at least 5 examples of your own. 