The simplest root form calculator
Calculator finds out the simplest form of given square root expression.

Beta version#

This online calculator is currently under heavy development. It may or it may NOT work correctly.
You CAN try to use it. You CAN even get the proper results.
However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.
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Symbolic algebra

ⓘ Hint: This calculator supports symbolic math. You can enter numbers, but also symbols like a, b, pi or even whole math expressions such as (a+b)/2. If you still don't sure how to make your life easier using symbolic algebra check out our another page: Symbolic calculations

Input data - expression under the root (radicand)#

Root radicand expression
(expression under the root)

Results - your root in the simplest form#

Square, which you enter
Show source8\sqrt{8}
Root in the simplest form
Show source222 \cdot \sqrt{2}
Root simplification step-by-step
1Show source8\sqrt{8}Factor expression under the root-
2Show source222\sqrt{2^{2} \cdot 2}Simplified power under rootThe power and n-th root can be treated as the same math operation: xpq=xpq\sqrt[q]{x^p} = x^{\frac{p}{q}}
3Show source222 \cdot \sqrt{2}ResultYour expression reduced to the simplest form known to us.

Some facts#

  • Root extraction is an operation inverse to exponentiation.
  • The root of n-th degree from the number x is equal to y when y raised to the n-th power gives x:
    xn=yyn=x\sqrt[n]{x} = y \Leftrightarrow y^{n} = x
    • nn - root degree,
    • xx - root argument (number under root function),
    • yy - root result (a number, that gives an root argument if raised to root degree).
  • The root of degree 2 is colloquially called the square root. It has been assumed that we can omit degree while writing square root symbol:
    x=x2\sqrt{x} = \sqrt[2]x
  • The root of degree 3 is colloqually called the cubic root.
  • The root from product is equal to the product of roots:
    xyn=xnyn\sqrt[n]{x y} = \sqrt[n]{x} \cdot \sqrt[n]{y}
  • The root from quotient is equal to quotient of roots:
    xyn=xnyn\sqrt[n]{\frac{x}{y}} = \frac{\sqrt[n]{x}}{\sqrt[n]{y}}
  • In order to render the root symbol xn\sqrt[n]{x} in the TeX\TeX language use command:

  • If you want to learn more about how to write different mathematical expressions, you can check out our other calculator: Quick TeX cheat sheet.

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