well, my mum and I have been arguing about this matter. SO - can -5 be considered the square root of 25? -5^2 = 25
please answer quickly!
please answer quickly!
-
You and your mom are BOTH right!
You can say that 5 is a square root of 25.
You can say that -5 is a square root of 25.
You can say that x=5 and x=-5 are solutions to the equation x^2 = 25.
You can say that 5 is THE PRINCIPAL square root of 25. -5 is NOT the principal square root of 25.
If you ask for THE square root of 25, the correct answer is 5, not -5.
You can say that RADICAL(25) = 5, but it is NEVER -5. Radical means the PRINCIPAL square root.
This all comes from some fairly advanced precalculus math that's typically covered in junior or senior yearh of high school math. They talk about "complex roots" of numbers. It gets worse when you start taking cube roots. Yes, there is only one real solution to the equation x^3 = 1. The ONLY real number that works, and the ONLY real cube root of 1, is 1.But did you know that there are two "hidden" solutions? These are "complex" numbers, and they involve the square root of -1. This number is NOT a real number, but it's given a name...the imaginary unit, or i.
You can see this by subtracting one from both sides to get:
x^3 - 1 = 0
Factor by difference of cubes and you get:
(x - 1)(x^2 + x + 1) = 0
You get one real solution on the left, and two complex solutions on the right. Don't worry if this goes over your head now.
Just know that if your teacher writes "radical 25", they mean 5 and only 5. If your teacher asks for a number that, when squared, gives 25...then they mean +/- 5. If they ask for THE square root of 25, they mean 5. If they ask for -A- square root of 25, which emphasis on 'a', then they mean +/- 5.
But -5 can never be called -THE- square root of 25. "The" implies something special. +5 is the special number, not -5.
You can say that 5 is a square root of 25.
You can say that -5 is a square root of 25.
You can say that x=5 and x=-5 are solutions to the equation x^2 = 25.
You can say that 5 is THE PRINCIPAL square root of 25. -5 is NOT the principal square root of 25.
If you ask for THE square root of 25, the correct answer is 5, not -5.
You can say that RADICAL(25) = 5, but it is NEVER -5. Radical means the PRINCIPAL square root.
This all comes from some fairly advanced precalculus math that's typically covered in junior or senior yearh of high school math. They talk about "complex roots" of numbers. It gets worse when you start taking cube roots. Yes, there is only one real solution to the equation x^3 = 1. The ONLY real number that works, and the ONLY real cube root of 1, is 1.But did you know that there are two "hidden" solutions? These are "complex" numbers, and they involve the square root of -1. This number is NOT a real number, but it's given a name...the imaginary unit, or i.
You can see this by subtracting one from both sides to get:
x^3 - 1 = 0
Factor by difference of cubes and you get:
(x - 1)(x^2 + x + 1) = 0
You get one real solution on the left, and two complex solutions on the right. Don't worry if this goes over your head now.
Just know that if your teacher writes "radical 25", they mean 5 and only 5. If your teacher asks for a number that, when squared, gives 25...then they mean +/- 5. If they ask for THE square root of 25, they mean 5. If they ask for -A- square root of 25, which emphasis on 'a', then they mean +/- 5.
But -5 can never be called -THE- square root of 25. "The" implies something special. +5 is the special number, not -5.