Square root principle calculator

Square root principle calculator DEFAULT

Square Root Calculator

Calculator Use

Use this calculator to find the principal square root and roots of real numbers. Inputs for the radicand x can be positive or negative real numbers. The answer will also tell you if you entered a perfect square.

The answer will show you the complex or imaginary solutions for square roots of negative real numbers.  See also the Simplify Radical Expressions Calculator to simplify radicals instead of finding fractional (decimal) answers.

Square Roots, odd and even:

There are 2 possible roots for any positive real number. A positive root and a negative root. Given a number x, the square root of x is a number a such that a2 = x. Square roots is a specialized form of our common roots calculator.

"Note that any positive real number has two square roots, one positive and one negative. For example, the square roots of 9 are -3 and +3, since (-3)2 = (+3)2 = 9. Any nonnegative real number x has a unique nonnegative square root r; this is called the principal square root For example, the principal square root of 9 is sqrt(9) = +3, while the other square root of 9 is -sqrt(9) = In common usage, unless otherwise specified, "the" square root is generally taken to mean the principal square root."[1].

Perfect Square Calculator

This calculator will also tell you if the number you entered is a perfect square or is not a perfect square.  A perfect square is a number x where the square root of x is a number a such that a2 = x and a is an integer. For example, 4, 9 and 16 are perfect squares since their square roots, 2, 3 and 4, respectively, are integers.

Example Square Roots:

  • The 2nd root of 81, or 81 radical 2, or the square root of 81 is written as $$ \sqrt[2]{81} = \sqrt[]{81} = \pm 9 $$.
  • The 2nd root of 25, or 25 radical 2, or the square root of 25 is written as $$ \sqrt[2]{25} = \sqrt[]{25} = \pm 5 $$.
  • The 2nd root of , or radical 2, or the square root of is written as $$ \sqrt[2]{} = \sqrt[]{} = \pm 10 $$.
  • The 2nd root of 10, or 10 radical 2, or the square root of 10 is written as $$ \sqrt[2]{10} = \sqrt[]{10} = \pm $$.

To calculate fractional exponents use our calculator for Fractional Exponents.

References

[1] Weisstein, Eric W. "Square Root." From MathWorld -- A Wolfram Web Resource. Square Root

Additional reading on square roots:

At Math is Fun: square root

 

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Posted: Friday 29th of Dec    

I've always wanted to learn square root property calculator, it seems like there's a lot that can be done with it that I can't do otherwise. I've browsed the internet for some useful learning tools , and consulted the local library for some books, but all the data seems to be targeted at people who already know the subject. Is there any tool that can help new students as well?
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Posted: Sunday 31st of Dec    

I really don’t know why God made math , but you will be delighted to know that someone also came up with Algebrator! Yes, Algebrator is a program that can help you crack math problems which you never thought you would be able to. Not only does it solve the problem, but it also explains the steps involved in getting to that solution. All the Best!
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Posted: Tuesday 02nd of Jan    

Even I’ve been through that phase when I was trying to figure out a way to solve certain type of questions pertaining to adding numerators and scientific notation. But then I came across this piece of software and I felt as if I found a magic wand. In a flash it would solve even the most difficult questions for you. And the fact that it gives a detailed and elaborate explanation makes it even more useful . It’s a must buy for every math student.
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evaluating formulas, angle complements and greatest common factor were a nightmare for me until I found Algebrator, which is really the best algebra program that I have come across. I have used it through many algebra classes – Intermediate algebra, Algebra 2 and Basic Math. Simply typing in the algebra problem and clicking on Solve, Algebrator generates step-by-step solution to the problem, and my math homework would be ready. I truly recommend the program.
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Calculator Tutorial 9: Square roots on a scientific calculator

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