What is the sign of the cube root of a positive number?

What is the the positive square root of a number indicated by the radical sign?

It is the principal square root.

What would be of the square root of a number if there is no sign in front of the square root symbol?

If unspecified, the square root is the principal root, which is the positive root.

What are forms of radical?

The radical symbol, otherwise known as the "square root sign", lets you take the nth root of any number.Any number can be placed above, and slightly to the left, of the square root sign, to indicate the nth root. For example, the cube root of 27 is 3.The number inside the square root sign (that which you are finding the square root of), is called the radicand.

What is the 2 in front of the square root sign?

The sign that is used for the square root is actually a root sign: the little 2 before it denotes that it is the square root. A little 3 would indicate it is a cube root, a little 4 that it is a fourth root and so on. However, conventionally, if no number is shown, it may be assumed that it is the square root.

Why do square roots come in pairs but cubed roots don't?

The square of a negative number is the same as the square of its positive counterpart, aka its additive inverse ( [-2]2 = 22 = 4), so every positive number has two square roots, a positive one and negative one (both 2 and -2 are square roots of 4). However, the cube of any number will always have the same sign as the original number (23 = 8, [-2]3 = -8). This all follows from simple arithmetic with signs. The product of any two negative numbers is positive, as is the product of any two positive numbers, while the product of a negative number and a positive number is negative. All squares, by definition, are the product of either two positive numbers or two negative numbers, and in either case, the product must be positive. But a cube is the product of a number and its square (x3 = x * x * x = x2 * x). But we already know that the square must be positive, whether original number is positive or negative. So the sign of the original number determines the sign of the cube (because a positive number times a positive number is positive and a positive number times a negative number is negative). If you apply that rule in reverse, then the sign of the cube root must be the same as the sign of the number you are taking the cube root of. Think of it this way. If you are trying to calculate the square root of a number, y, you are looking for another number, x, for which it is true that x * x = y. For any positive number y, there are always two values of x that satisfy that equation, with one being positive and the other being negative, but both having the same absolute value. And therefore, every positive number has two square roots. On the other hand, if you are trying to find the cube root of a number, y, you are looking for a number, z, for which it is true that z * z * z = y. For any number, y, either positive or negative, there will be only one value of z that satisfies that equation. Therefore, every number, positive or negative, has just one cube root. Actually, technically, once you get into higher mathematics, what is really going on is that every number has 3 cube roots, but they all just happen to have the same value. In fact, for any "degree" of root (square root, cube root, 4th root, 5th root, ... 100th root, ...) the number of roots of a number is exactly equal to the degree of the root (a number will have 4 4th roots, 5 5th roots, 10 10th roots, 99 99th roots, etc.) But, if the degree of the root is odd, then all of the roots will have the same value, while if the degree is even, the roots will be evenly split between two values that are the additive inverses of each other. For example, the 5th roots of -243 are -3, -3, -3, -3, and -3, while the 6th roots of 64 are 2, 2, 2, -2, -2, and -2. Note also that negative numbers cannot have any roots of any even degree (square roots, 4th roots, 6th roots, etc.) Actually, even that's not true when you get into really advanced math. Even negative numbers have even-degree roots, it's just that the roots are not real numbers. They are "imaginary" numbers. This is, I'm sure, way beyond your level of education in mathematics, and I'm not trying to confuse you. But if I hadn't included these last two paragraphs, some wise-guy mathematician would come along and "correct" me, and in the process probably confuse you even more. For your purposes, however, just ignore the last two paragraphs.

How does the sign of a determine the number of real fourth roots of a and the number of real fifth roots of a?

If "a" is positive, it will have two fourth roots, one will be positive and one will be negative it will have one fifth root, which will be positive. If "a" is negative, it will have one fourth root, which will be negative. it will have one fifth root, which will be negative.

What is the symbol used to indicate the positive square root of a number?

It is the RADICAL SIGN , its definition is - the symbol used to indicate a nonnegitive square root.

How do you find the square roots of fractions?

Square rootsTo find the square root of a number, you want to find some number that when multiplied by itself gives you the original number. In other words, to find the square root of 25, you want to find the number that when multiplied by itself gives you 25. The square root of 25, then, is 5. The symbol for the square root is . Following is a partial list of perfect (whole number) square roots.Note: If no sign (or a positive sign) is placed in front of the square root, the positive answer is required. No sign means that a positive is understood. Only if a negative sign is in front of the square root is the negative answer required.A fraction, or fractional number, is used to represent a part of a whole. Fractions consist of two numbers: a numerator (which is above the line) and a denominator(which is below the line).So to work out the square root of a fraction you find the square root of the numerator and put it above the square root of the denominator.

What is a square root symbol is called?

The general case is just called "Root" and it continues to increase to "Square Root" then to "Cube Root" and so on.

If a negative number squared is positive why isn't the square root of a positive number negative?

When a negative number is squared, the negative sign is essentially squared along with the number, resulting in a positive value. However, when taking the square root of a positive number, we are looking for the value that, when squared, gives us the original positive number. Since both a positive and negative number can square to the same positive value, the convention is to consider the principal (positive) square root by default. The negative square root is also a valid solution in many contexts, but for simplicity and consistency, the positive square root is typically chosen.

How do you find the principal square root of a monomial?

Say the monomial is 4a squared. To find the square root to must do each part seperately. So square root of 4 is 2 and the square root of a-squared is |a| because we do not know the sign of a. The answer is 2|a|. If there is anything that cannot be "square rooted" then it would stay under a square root sign and just multiply by 2a as well. The principal root of a number is only its positive root (you can understand that you are looking for the principal root from the sign in front of the radical, which is a positive one)

The square root cube of 216?

if you mean the cubed root, the answer is 6. i would show you the calculations but unfortunately i have no idea how to do a cubed root sign. :S :)