Radical Calculator

The radicand. Negative values are allowed; an even root of a negative number is imaginary.
Multiplies the root, so 3 with 18 gives 3 sqrt(18) = 9 sqrt(2).
Root
8.485281
Square Root and Nth Root Calculator
Rounded root
8.485281
Exact (simplified radical)
6 sqrt(2)
Factor outside the radical
6
Radicand left inside
2
Perfect power?
No
Negative branch
-8.485281
Check (root raised to the index)
72
Expression
sqrt(72) = 6 sqrt(2) = 8.48528137424
Worked out from NIST Digital Library of Mathematical Functions, 4.2(i) Powers and Roots and 1 other source.

How this is worked out

4 steps
  1. Prime-factorise 72 and pull out every complete group of 2: 72 = 6^2 x 2.
  2. So the exact form is 6 sqrt(2).
  3. Decimal value: 8.48528137424 = 8.48528137424.
  4. An even root has two real branches: +8.48528137424 and -8.48528137424.

Results are general information, not financial, tax, legal, medical or engineering advice.