ZovaTool

Root Calculator

Result

√(72)
8.485281
Exact (surd form)
6√2
x^(1/n)
8.485281
Verify r^n
72
Rationalize 1/√x
√72/72
Decimal (12 dp)
8.485281374239

Step-by-step (surd simplification)

Step 1
2√72 — factor inside: 72 = 2^3 × 3^2
Step 2
Group factors in sets of 2 → take out √[n]( ) what reaches multiple of 2
Step 3
Simplified surd: 6√2
Step 4
Decimal value: 8.485281

Common roots

√2
1.414214
√3
1.732051
√5
2.236068
√7
2.645751
√10
3.162278
∛2
1.259921
∛3
1.44225
∛5
1.709976
∛10
2.154435

How to use the Root Calculator

  1. Enter the radicand x.
  2. Enter the index n (n=2 for square root, n=3 for cube root).
  3. Result includes verification by raising back to the power.
  4. Negative radicands with even index are flagged as non-real.
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Square, cube, and n-th roots

An n-th root undoes an n-th power: if y = x^n then x = y^(1/n) = ⁿ√y. So square root, cube root, and so on are all special cases of one formula.

Internally roots are computed via exp(ln(x)/n), which is fast and accurate for any positive radicand.