The square of 25 is 25 x 25 = 625. The principal square root of 25 is 5.
The principal root of a number is the positive real square root of the number - if it exists. Since -25 is negative, it does not have a real square root. Its square roots are the imaginary numbers +/-5i where i is the [imaginary] square root of -1. i is neither positive nor negative and so neither +5i nor -5i is a principal root.
A number will have both a positive and negative square root 5 x 5 = 25 and -5 x -5 = 25.
sqrt(15) + sqrt(25) = 5 + sqrt(15) = 8.873 (using principal roots only).
The square root of fraction 20 over 25: = √20 ...√25 = √4(5) ......5 = 2√5 .....5 or 2 square root of 5 over 5
It is 25
The square of 25 is 25 x 25 = 625. The principal square root of 25 is 5.
The principal root of a number is the positive real square root of the number - if it exists. Since -25 is negative, it does not have a real square root. Its square roots are the imaginary numbers +/-5i where i is the [imaginary] square root of -1. i is neither positive nor negative and so neither +5i nor -5i is a principal root.
Restricting the discussion to real numbers for now. In this case, the square root is only defined for non-negative numbers; the principal square root of a positive number is the POSITIVE square root. For example, both +5 and -5 are square roots of 25, since both - when squared - give you 25. But the positive square root (+5) is called the principal square root, and if you write the square root symbol, that's the number usually meant.
That refers to the positive root, at least if you take the root of a positive number. For example, 25 has two square roots - two numbers which, when squared, give 25. The positive one (+5) is called the principal square root (or 2nd. root).
A number will have both a positive and negative square root 5 x 5 = 25 and -5 x -5 = 25.
sqrt(15) + sqrt(25) = 5 + sqrt(15) = 8.873 (using principal roots only).
The square root of fraction 20 over 25: = √20 ...√25 = √4(5) ......5 = 2√5 .....5 or 2 square root of 5 over 5
Well, honey, to find the square root of 625 over 36, you first find the square root of the numerator (625) which is 25, and the square root of the denominator (36) which is 6. So, the square root of 625 over 36 is 25 over 6. Math doesn't have to be as complicated as your ex's drama, darling.
The square root of 8 over 25 is irrational, and real.
There is a partial relationship. The principal square root of a perfect square is the number itself. For example, the principal square root of 5^2 = the principal square root of 25 = the positive element in {-5, 5} = 5. The converse is not true. The number 3, for example, has a square root which are approx -1.7321 and 1.7321. But the square of either of these numbers is 3, but that is not a perfect square since it is not the square of an integer.
The square root of a positive number results in a positive number. For example, the square root of 25 is 5. * * * * * Not true! There are two real square roots for every positive number: one positive and one negative. -5 is as much a square root of 25 as +5 is. However, the positive root is the principal root and so is often presented as the only root.