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To simplify a surd, remember that
sqrt(a*b) = sqrt(a)*sqrt(b)
If either a or b are square numbers, you can simply write its square root. Hence, to simplify a surd, you must look for any factors of the number inside the square root that are sqaure numbers.
sqrt(20) = sqrt(4*5) = sqrt(4)*sqrt(5)
sqrt(4) = 2 therefore sqrt(20) = 2sqrt(5)see more
If a set of equations has more unknowns than equations, you cannot get a value for each unknown. However, you can find the relationships between the variables.
Start by rearranging one variable in terms of the others and then plug that equation into the others, eliminating one variable. You will then be able to link the rest of the variables together in terms of each other.
Finally, set one variable as a parameter, say u, and give the values of all the variable in terms of that uniting parameter.
For example, you will end up with something like:
x = 2u - 1
y = 1/2u + 4
z = usee more
For all quadratic equations, you can use the quadratic formula. Given an equation of the form ax2+bx+c, you can plug those values into this formula:
x1, x2 = (-b +/- sqrt(b2 - 4ac)) / 2a
Note: the term b2 - 4ac is called the determinant and must be greater than 0 for your equation to have any solutions.see more