About Simplify Radical Calculator
This simplify radical calculator writes a square root, cube root or higher root in simplest form by pulling out every perfect power, and shows each step. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The page opens on √180. Since 180 = 2² × 3² × 5, the 2s and the 3s come out and the 5 stays: 6√5, about 13.416408. A radical is in simplest form when no factor under the root is a perfect power and there is no fraction under the root.
Set the root index to 3 or more to simplify cube roots and higher roots in the same way. Fractions are rationalised, so the denominator never contains a root.
How to use Simplify Radical Calculator
- Choose Square root, Cube root, nth root or Simplify radical.
- Type the number. A whole number, a decimal or a fraction all work, and negatives are allowed.
- For an nth root, type the root index. Choose how many decimal places you want.
- Read the exact form and the decimal at the top.
- Open the steps to see the prime factorization and the pairs taken out of the root.
Features
- Simplified radical form with the prime factorization shown: √72 = 6√2.
- Decimal to up to 100 places, computed exactly with integers.
- Square roots, cube roots and nth roots up to index 100.
- Imaginary results for negative numbers under even roots, and real roots for odd ones.
- Perfect squares and perfect powers are recognised and shown exactly.
- Decimals and fractions accepted, with the denominator rationalised.
- Step-by-step working in KaTeX and a copy button.
Simplest radical form
Split the radicand into a perfect power times the rest, then take the root of the perfect power.
√180 = √(36 × 5) = √36 × √5 = 6√5Worked examples
√180 gives 6√5 ≈ 13.416408
180 = 36 × 5.
√(5/8) gives √10/4
The denominator is rationalised: √(5/8) = √40 / 8 = 2√10 / 8 = √10 / 4.
Privacy: how it works
- Everything is calculated by code running in your browser tab. The numbers you enter are not sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- To estimate a square root by hand, find the two perfect squares around it. √50 is between √49 = 7 and √64 = 8, so it is a little over 7.
- A decimal that neither ends nor repeats means the root is irrational, which is true of the root of any number that is not a perfect power.
- Check a decimal root by squaring it. The result should be very close to the number you started with.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Numbers are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Numbers are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
When is a radical in simplest form?
When no factor of the number under the root is a perfect power of the index, and no root is left in a denominator.
How do I simplify a radical quickly?
Find the largest perfect square that divides the number. For 180 it is 36, so √180 = √36 × √5 = 6√5.
More Square Root Calculator pages
- Square Root CalculatorEnter a number to get its square root in simplest radical form and as a decimal, with the working.
- Cube Root CalculatorEnter a number to get its cube root, exact where possible, with the working.
- Nth Root CalculatorEnter a number and a root index to get the nth root with the working.
- Square Root of 2The square root of 2 is about 1.41421356, and its digits never end or repeat.
- Square Root of 3The square root of 3 is about 1.7320508, and its digits never end or repeat.
- Square Root of 72The square root of 72 simplifies to 6√2, which is about 8.4853.