24 Square Root Of 3

(fill up in either box above to explore more well-nigh foursquare roots)
Answers are rounded to vii decimal places.

Valid input:

positive numbers: ii
negative numbers: -3
imaginary numbers: -7i
complex numbers: 8+9i

Notes:

The square root calculator provides the primary foursquare root (the positive square root which is almost commonly used). Multiplying the principal square root past -i will provide the negative square root if needed.
The square root of a negative number results in an imaginary number noted by the letter "i".

Square Root:

The square root of a number is a value that when multiplied by itself equals the original number. Example: The square root of 9 = iii. Thus: 3 x 3 = 9.

Where A and B are valid numbers:
A is the square root of B if: A 10 A = B

Square Root Symbol / Square Root Sign:

The square root of a number Due north is usually represented by: √ Due north
It can also be represented by: ²√ N
In exponential annotation, it can exist represented by: N^1/2
"Square root" can exist abbreviated as "sqrt" Case: sqrt(2) = 1.4142136

Thus all of the post-obit are equivalent:
Square Root of N = √ N = ²√ N = Northward^1/2 = sqrt(Northward)
(With the exception that the radical sign √ refers to the principal (positive) foursquare root simply.)

See: square root symbol if you need to add the symbol to a text document.
How are square roots used:

Square roots can be used:
- to solve for the altitude between 2 points (Pythagorean Theorem)
- to solve for the length of a side of a right triangle (Pythagorean Theorem)
- to find the solutions to quadratic equations
- to find normal distribution
- to detect standard deviation
- basically to solve for a squared variable in an equation
If yous see an equation like Due north² = 27 , you lot can solve for N by taking the square root of 27 which gives Northward = 5.1961524

How to Calculate the Square Root of:

A Positive Number:
The square root of a positive number can be calculated past:
1. square root figurer to a higher place
2. handheld calculator
3. spreadsheet
4. square roots without a calculator
A Negative Number:
To calculate the foursquare root of a negative number, find the foursquare root of the aforementioned positive number and multiply past "i". ( where i represents an imaginary number and i = square root of -ane)
Example: square root of -5
= (square root of 5) x (square root of -1)
= (square root of v) 10 (i)
= two.236068 x i
= two.236068i
An Imaginary Number:
To summate the foursquare root of an imaginary number, find the square root of the number equally if it were a real number (without the i) and then multiply by the square root of i (where the square root of i = 0.7071068 + 0.7071068i)
Example: foursquare root of 5i
= (square root of v) x (square root of i)
= (2.236068) x (0.7071068 + 0.7071068i)
= 1.5811388 + ane.5811388i
A Circuitous Number:
To detect the square root of a complex number, employ the following equation:
Square root (a + bi) = c + di
Where:
c = (1/square root of 2) 10 square root of [ (square root of(a²+b²)) + a ]
d = (sign of b/square root of 2) ten foursquare root of [ (square root of(a²+b²)) - a ]
Example: the square root of 3-5i = c + di
c = (1/foursquare root of 2) x square root of [ (square root of(3²+(-v)²)) + 3 ]
c = 2.1013034
d = (-1/square root of 2) x square root of [ (square root of(3²+(-5)ⁱⁱ)) - 3 ]
d = -one.1897378
Thus: square root of 3-5i = 2.1013034 - 1.1897378i

Need to calculate the square root of a number with a handheld figurer or looking to buy a new calculator?

Most handheld calculators have a foursquare root part.
Below is a review of some that are recommended and how to utilise them.

Graphing Computer:

Texas Instruments TI-84 Plus Graphing Calculator

To take the square root of a number, press [2nd] (the secondary function key) so [ √ ] (the radical symbol key which is used to have the square root of a number) and so the number that you want to find the square root of and then the [ENTER] fundamental.
Example:
To find the foursquare root of 2, push:
[2d] [ √ ] ii [ENTER]
This will give you the answer of: 1.414213562 if done correctly.

(Note: This same method will also work with TI-83 and TI-81 calculators)

Graph:
To graph the square root function y = √x
Printing [Y=] [2ND] [ √ ] [Ten,T,O,n] [GRAPH]

Apply the [Trace] key and Arrow keys to trace and show values along the graph.

(To run across what the graph looks like on this estimator, click the show graph button below the calculator image on this folio.)

Pros:
It tin be used on many college entrance exams (check your test criteria).

It is a popular computer. (If you need help, the likelihood of finding someone who knows how to use it is college).

The display shows seven lines of input/output. Long equations tin can be viewed and checked. (This is a overnice benefit that graphing calculators accept compared to scientific calculators that may only have a single line brandish.) Some other benefit of having a big display is you tin can compare your current respond to past answers that are all the same on the screen. This can often help yous discover an input error that may have otherwise gone unnoticed.

Cons:
It is bulkier than a scientific calculator.
It costs effectually $85 (USD) more than a scientific calculator.

Cost:
Best price for this calculator as of nine-2-2014 is around $94.00 (USD).
Casio Graphing Reckoner (fx-9750GII)

To take the square root of a number, press [SHIFT] and and then [ √ ] (the radical symbol is to a higher place the x² primal) and then the number that you want to find the foursquare root of and then the [EXE] key.
Case:
To notice the square root of 2, push:
[SHIFT] [ √ ] 2 [EXE]
This will give y'all the answer of: one.414213562 if entered correctly.

Graph:
To graph the square root function y = √x
Press [Card], select Graph, [EXE]
[SHIFT] [ √ ] [10,O,T] [EXE] [F6]
Utilize the [F6] key to toggle between the graph screen and the equation screen.

Use the [F1] key and Pointer keys to trace and show values along the graph.

(To encounter this graph, click the evidence graph button below the calculator prototype on this page.)

Pros:
The cost is one-half the price of a TI-84 calculator.
It is a piffling smaller than the TI-84 calculator.
It tin can be used on many college entrance exams (check your exam criteria).
The display shows 7 lines of input/output.

Cons:
It is not as pop as the TI-84 calculator. (Information technology may be harder to find someone to help if you accept a question virtually how to employ the computer.)

Toll:
Best cost as of 9-2-2014 is around $42.74 (USD).

Scientific Reckoner:

Texas Instruments TI-36X Pro Scientific Computer

To have the square root of a number, press [2ND] (the secondary function primal) and then [ √ ] (the radical symbol fundamental which is used to take the foursquare root of a number) and and so the number that y'all want to discover the square root of then the [ENTER] primal.
Note: If your estimator is in "Math Print" mode, the display will show √ ii as the answer. To convert this reply to a decimal number, press the [<>~] key (the "Answer Toggle" central) which is the key above the [ENTER] key.
Example:
To find the square root of two, button:
[2ND] [ √ ] 2 [ENTER]
(If in "Math Impress" mode, printing [<>~] afterwards pressing the [ENTER] cardinal.)
This will brandish the answer of: 1.414213562

Pros:
Information technology is good if a graphing calculator is not permitted.
It is smaller and lighter than a graphing calculator.
The brandish shows iv lines of input/output. Some scientific calculators simply show one line of input/output.

Cons:
The symbols shown on the office keys ( + , - , etc.) may be hard to come across because they are the same silverish color as the keys.

Toll:
Best price for this calculator on 9-2-2014 is around $19.99 (USD).

Math Help / Math Tutor

If y'all need help with math:

At that place are a lot of online resources that are costless to use and are available when you need them. Some sites have online courses, instructional videos, and even math games to help y'all learn more than nigh math.
Ask someone who is skillful at math to help. If y'all tin't find anyone who tin can assistance, a math teacher at a local school may be able to help or recommend a math tutor in your area.
A local library may exist able to help non but with advisory books just they may exist able to recommend a math tutor as well.
There are several websites that can help you find a local tutor if you would like in-person tutoring. Also, some tutors are able to help from a remote location if needed. Prices are typically between $10 to $l (USD) per hour. E'er inquiry and endeavour to detect reviews, ratings, or feedback from others who accept used a particular tutor before making a selection.