About Square Root of 72
The square root of 72 is not a whole number, but it simplifies. This page opens on it and shows every step of reducing it to simplest radical form. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
Factor 72 into primes: 72 = 2³ × 3². Group the pairs: (2² × 3²) × 2. The pairs leave the root as 2 × 3 = 6, and the single 2 stays inside, so √72 = 6√2. As a decimal, that is 8.4852813742.
A shortcut is to find the largest perfect square that divides 72. That is 36, and √72 = √36 × √2 = 6√2. Using the largest one in a single move avoids repeated simplifying.
How to use Square Root of 72
- 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.
Simplifying √72
Write 72 as a perfect square times the rest.
72 = 36 × 2
√72 = √36 × √2 = 6√2 ≈ 8.485281Worked examples
√72 gives 6√2 ≈ 8.4852813742
72 = 2³ × 3².
√(72/2) gives 6
72 / 2 = 36, which is a perfect square.
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.
What is the square root of 72 in simplest radical form?
6√2. Because 72 = 36 × 2 and √36 = 6.
Is the square root of 72 rational?
No. 72 is not a perfect square, so √72 is irrational. Its decimal, about 8.485281, never ends or repeats.
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.
- Simplify Radical CalculatorEnter the number under the root and get the radical in simplest form with the steps.
- 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.