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### High School Mathematics6.15 Problems on Square Root - I

 Example: Find the square root of (x2 + 7x + 12)(x2 + 10x + 24)(x2 + 9x + 18). Solution: Take the factors, x2 + 7x + 12 = x2 + 4x + 3x + 12 = x(x + 4) + 3(x + 4) = (x + 3)(x + 4) x2 + 10x + 24 = x2 + 4x + 6x + 24 = x(x + 4) + 6(x + 4) = (x + 4)(x + 6) x2 + 9x + 18 = x2 + 6x + 3x + 18 = x(x + 6) + 3(x + 6) = (x + 3)(x + 6) Therefore, (x2 + 7x + 12)(x2 + 10x + 24)(x2 + 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.
 Q 1: Find the square root of (12x2 + 23x + 10)(15x2 + 13x + 2)(20x2 + 29x + 5).(4x + 5)(3x + 2)(5x + 2)(4x + 3)(3x + 2)(5x + 1)(4x + 5)(3x + 2)(5x + 1)(4x + 5)(3x + 4)(5x + 1) Q 2: Find the square root of (x2 + 10x + 16)(x2 + 11x + 24)(x2 + 5x + 6).(x + 2)(x - 8)(x + 3)(x + 2)(x + 8)(x + 3)(x + 2)(x + 8)(x - 3)(x - 2)(x + 8)(x + 3) Q 3: Find the square root of (6x2 + 16x + 8)(8x2 + 20x + 8)(12x2 + 14x + 4).(3x + 2)(2x + 4)(3x + 3)(4x + 2)(2x + 4)(4x + 3)(3x + 2)(2x + 4)(4x + 3)(3x + 2)(x + 4)(4x + 3) Q 4: Find the square root of (x2 - 2x - 15)(x2 - 5x - 24)(x2 - 13x + 40).(x - 8)(x - 5)(x + 3)(x - 8)(x + 5)(x + 3)(x + 8)(x - 5)(x + 3)(x - 8)(x - 5)(x - 3) Q 5: Find the square root of (x2 + x - 12)(x2 - x - 20)(x2 - 8x + 15).(x - 5)(x - 3)(x - 4)(x - 5)(x + 3)(x + 4)(x - 5)(x - 3)(x + 4)(x + 5)(x - 3)(x + 4) Q 6: Find the square root of (x2 - 4x + 3)(x2 - 12x + 27)(x2 - 10x + 9).(x - 9)(x - 3)(x + 1)(x - 9)(x + 3)(x - 1)(x + 9)(x - 3)(x - 1)(x - 9)(x - 3)(x - 1) Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!

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