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Q: Positive numbers have two square roots a principal square root and its?

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The principal root is the positive square root.

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).

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.

A positive number has two square roots, that is, there are two solutions to an equation like x2 = 100. The "principal square root" refers to the positive solution.

They are called real numbers. Negative square roots must be complex numbers.

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.

true

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.

A positive number has two square roots, its principal (positive) root and its negative root. This is because a negative number multiplied by a negative number equals a positive number. In this instance, the square roots of 256 are 16 and -16.

False

True

Every positive number has TWO square roots. The principal square root is the positive number which, when multiplied by itself, gives the number in question. But its negative equivalent will also be a square root. For example, the number 4 has 2 as the principal sqrt but -2 is also a sqrt of 4

This is because if you multiply two negative numbers you get positive.

In the context of square roots, positive and principal are equivalent. So one of these adjectives is redundant. Sqrt(5) = 2.24 (to 2 dp)

The positive square root of 115 lies between the positive square roots of 114 and 116.The positive square root of 115 lies between the positive square roots of 114 and 116.The positive square root of 115 lies between the positive square roots of 114 and 116.The positive square root of 115 lies between the positive square roots of 114 and 116.

The second root would be the negative of the principal root.

Negative numbers do not have "real number" square roots.However, they will have two roots (when using imaginary numbers) as do other numbers, where a root including i(square root of -1) is positive or negative.

You call them principal square roots.

Zero is the only number that has only one square root.The square root of zero is zero.All other numbers have two square roots.The square roots of 4 are 2 and -2. Two is referred to as the "principal" square root.When you get to the grade that discusses imaginary/complex numbers, you'll learn that negative numbers also have square roots. The square roots of -4 are 2i and -2i. 2i is the principal square root.

Because multiplying negative numbers together gives a positive answer. So the square root of nine is both three and minus three.

Numbers with square roots that are whole numbers

The answer depends on "different from WHAT?" Positive cube roots, or negative square roots?

a is a real number since we use just letters to represent real numbers. if a > 0, then its square root is also a real number, so it has two square roots, one positive and one negative. Be careful when you use the radical sign, because it is looking only for the principal square root of a, which is the positive one. if a < 0, then its square root is an imaginary number.

The numbers 1 and negative 1 (-1) are both square roots of positive 1.The square root of negative 1 is the "imaginary" number i.

The principal square root is a positive number which, when multiplied by itself, gives the original number. The second square root is the negative of the principal square root. So, for example, starting with 144. The principal square root is 12 because 12*12 = 144 and the second square root is -12.