8.3
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The Square Root of 4761 is 69
The quadratic equation provides solutions for the generalized equation ax2 + bx + c = 0. The solution(s) are (-b +/- square root ( b2 - 4ac)) / 2a. Plugging in a=1, b=3, and c=-15 (from x2 + 3x -15 = 0) you get... (-3 +/- square root (32 - 4(1)(-15)) / 2(1) ... or ... (-3 +/- square root (9 + 60)) / 2 ... or ... (-3 +/- square root (69)) / 2 ... or ... about -3 +/- 8.3 Since 69 is positive, the square root (69) is real, at 8.3 This equation has two real roots, x=5.3 and x=-11.3 If the discriminant (b2 - 4ac) were zero, there would be one real root. If it were negative, there would be one real root and one imaginary root, i.e. a complex conjugate.
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The square root of 15 times the square root of 5 can be simplified as the square root of (15 * 5), which equals the square root of 75. The square root of 75 can be further simplified as 5 times the square root of 3. Therefore, the square root of 15 times the square root of 5 is equivalent to 5 times the square root of 3.