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#1 2024-04-30 10:29:04
- mathxyz
- Member
- From: Brooklyn, NY
- Registered: 2024-02-24
- Posts: 1,053
Principal Square Root of A Number
If x is a nonnegative real number, the nonnegative number y such that y^2 = x is the principal square root of x ,and is denoted by y = sqrt{ x }.
What?
This definition is not clearly stated.
What on earth does it mean?
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#2 2024-04-30 14:05:39
- G4B_r09
- Novice
- From: Brazil
- Registered: 2024-04-28
- Posts: 3
Re: Principal Square Root of A Number
Heya!
A number has two square roots: one negative and one positive. The principal square root is the positive root, and so it is nonnegative. Basically y is the nonnegative number which multiplied by itself gives x as a result. The principal square root of 4 is 2 (2 * 2 = 4), the principal square root of 9 is 3 (3 * 3 = 9), and so on. All nonnegative real numbers have a square and a square root. The negative real numbers only have a square, they don't have a square root. An important thing to note is that the two roots of a number (the positive and the negative) are always opposite, they have the same numerical value but are in opposite sides on the number line. This can also happen in quadratic functions and equations, but not always, since these involve numerical expressions and more complicated square roots.
Hope I could help ya! 
"For God so loved the world, that He gave His only Son, so that everyone who believes in Him will not perish, but have eternal life." John 3:16 
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#3 2024-05-01 04:46:36
- mathxyz
- Member
- From: Brooklyn, NY
- Registered: 2024-02-24
- Posts: 1,053
Re: Principal Square Root of A Number
Heya!
A number has two square roots: one negative and one positive. The principal square root is the positive root, and so it is nonnegative. Basically y is the nonnegative number which multiplied by itself gives x as a result. The principal square root of 4 is 2 (2 * 2 = 4), the principal square root of 9 is 3 (3 * 3 = 9), and so on. All nonnegative real numbers have a square and a square root. The negative real numbers only have a square, they don't have a square root. An important thing to note is that the two roots of a number (the positive and the negative) are always opposite, they have the same numerical value but are in opposite sides on the number line. This can also happen in quadratic functions and equations, but not always, since these involve numerical expressions and more complicated square roots.
Hope I could help ya!
I appreciate your time and effort..
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