# Why would one use root sum square for a calculation?

The square root of the sum of the squares (RSS) can be used to calculate the aggregate accuracy of a measurement when the accuracies of the all the measuring devices are known. The average accuracy is not merely the arithmetic average of the accuracies (or uncertainties), nor is it the sum of them.

Let's say you are conducting a test to verify the resistance of a coil. The coil is built to have a resistance to within one percent of its nominal value. Further, say you have an ohm meter that is accurate to within 0.5 percent of the measured value, but the test leads introduce an uncertainty of two percent. What is the inherent accuracy of any measurement that you make with that set-up?

Use RSS to figure it out.

RSS = SQRT(0.0052 + 0.022) = 0.0206 = 2.06 percent. Note how the RSS result in this case is greater than the largest of the values under the radical. (BTW, that test rig isn't a very good one for verifying whether the coil is within spec. The rig's uncertainty is more than two times the tolerance of the coil.)

### What is the square root of 261?

The square root of 261 can be written as the square root of (9x29). Now the product rule for square roots tells us this is the same as square root of 9 multiplied by the square root of 29. This is 3xsquare root of 29. The square root of 29 can only be approximated. One approximation to square root of 261 is 16.1555.

### 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…

### How do you do square roots with negatives?

Treat it like a positive and add an i. Explanation: The square root of negative nine is equal to the square root of nine times negative one is equal to the square root of nine times the square root of negative one. The square root of negative one represented by an italic lower case i. The square root of negative nine is 3i. √-9 = √9 * -1 = √9 * √-1 = 3i

### What is the nonnegative square root of a number?

Definition of Square Root: The Square Root of a number 'X' is equal to 'A' when X=A*A By definition, the square root of a positive number has two answers, one negative and one positive, that have equal magnitudes. i.e. The square roots of 4 are 2 and -2. The Non-Negative Square Root is simply asking for the positive root.

### Can the square root of x be added to the square root of 3x?

No. The Square root of x is not the value of x. So it can not be simplified beyond: Root X + root 3x Yes. The square root of 3x equals the square root of 3 times the square root of x, so when you add another square root of x, you can factor out the square root of x, thereby simplifying the expression to the square root of x times the sum of one…

### What is the square root of a negative number plus the square root of a negative number?

Nothing. You cannot have a square root of a negative number. The square root of negative one is called i, but i is an imaginary number. It does not exist and does not follow the properties of real numbers. (For example, if a and b are positive, then the square root of a times the square root of b is the square root of ab. But the square root of -7 is not the square…

### How you find the square root of 5?

Answer: With great difficulty because it's an irrational number that can't be expressed as a fraction Answer: The same way you find the square root of any other number. It is preferable to use a calculator, since the calculation is quite involved. One method to calculate the square root is to try out squaring different numbers, until you get one that is close enough to 5 in this case. There are more efficient methods, but…

### What is the physical meaning of -1 aka the square root of -1 Does it have any physical existence and if not then why is it used to describe some real physical quantities like some terms in electricit?

The square root of -1 is represented by the letter i. This can be useful because it allows one to solve problems that would normally be unsolvable due to the presence of a negative radical at some point during the calculation. As long as the solution does not contain an i, it can be used in practical applications.

### What is the square root of negative twenty?

Because the Square Root of negative 1 = i (The imaginary square root of negative 1.) and where if the square root of one number and of another number are multiplied together, the answer is equal to the square root of the two numbers combined. (Square root of 8 times the square root of 5 equals the square root of 40.) So... √(-20) =√20×√(-1) =√4×√5×i =2i(√5) The answer is 2i times the square root of…

### What is the nonenegative square root of a number?

Every number has two square roots ... a positive one and a negative one. Example: +2 and -2 are both square roots of 4, because when you multiply either of them by itself, the answer is 4. The positive square root of a number is the square root that's not negative. The non-negative square root of a number is the positive one.

### What is the square root of a positive?

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.

### Can numbers that are not square have square roots?

Yes and no. It depends on your definition of square root. By the actual one, yes. All non-negative numbers have a square root. That square root might be irrational but it has a square root, nonetheless. 10 isn't a square number because there's no integer that can be squared to make ten but 10 definitely has a square root: 3.16227766....... If by square root you mean an integer square root, then no. If a number…