how do you solve an equation by extracting square roots? my book can't help, and the teach can't explain it so i understand it.
2 answers
to take out square roots, just basically square the number. for example to take square root of four is 2 but to take out the square root is square the four and your answer remains 4
If x^2 = a, then:
x = ± sqrt[a]
If x^2 + p x + q = 0, then you want to get rid of the linear p x term. You can do that by substituting:
x = y - p/2
The linear term in y then cancels and you can solve for y by taking the square root.
Third and fourth degree equations can be solved too by extracting roots. But equations of fifth or higher degree cannot (in general) be solved by extracting roots.
x = ± sqrt[a]
If x^2 + p x + q = 0, then you want to get rid of the linear p x term. You can do that by substituting:
x = y - p/2
The linear term in y then cancels and you can solve for y by taking the square root.
Third and fourth degree equations can be solved too by extracting roots. But equations of fifth or higher degree cannot (in general) be solved by extracting roots.
4 answers