Skip to main content

Square Root Calculator

Math Calculators

√x — real square roots with precision

Quick Answer

Square Root Calculator: √x — real square roots with precision. Square Root Calculator uses standard math formulas to compute accurate results instantly.

√72

8.48528137

simplified：√72 = 6√2

Perfect square?No
Between squares64 ~ 81
n²72
Cube root ∛n4.160168

Simplification steps

  1. 1Factorize: 72 = 2 × 2 × 2 × 3 × 3
  2. 2Pair up equal factors; each pair comes out as one factor
  3. 3√72 = 6√2 ≈ 8.485281

Position between 8² and 9²

closer to 8²
closer to 9²

√72 ≈ 8.4853

Perfect squares 1²–15²

1² = 12² = 43² = 94² = 165² = 25
6² = 367² = 498² = 649² = 8110² = 100
11² = 12112² = 14413² = 16914² = 19615² = 225
Mental math: to estimate √n, bracket it between perfect squares and interpolate — √50 ≈ 7 + (50−49)/(64−49) ≈ 7.07 (true 7.0711).

Common roots (memorize first 4)

√2

1.41421356

√3

1.73205081

√5

2.23606798

√7

2.64575131

√10

3.16227766

√11

3.31662479

√13

3.60555128

√17

4.12310563

💡 Estimation trick: find nearest perfect squares — √50 is between 7² and 8², closer to 7.1. Simplification: pull out square factors (√72 = √36·√2 = 6√2). To add radicals, simplify first: √8 + √18 = 2√2 + 3√2 = 5√2.

Was this tool helpful?

Average 5 · 1 rating

How to Use

  1. Enter values or expressions: type directly into the Square Root Calculator — keyboard friendly.
  2. Instant results: everything computes live as you type, no button needed.
  3. Follow the steps: the result panel shows full working and formula substitution.
  4. Copy or recompute: one-click copy; change any input to recalculate instantly.

Key Points

  • Square Root Calculator is a free online math tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: √x — real square roots with precision.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Square Root Calculator formula

Square Root Calculator uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Square Root Calculator?
Open the page and fill in the input fields — results update automatically. √x — real square roots with precision.
Are the results accurate?
Yes. All calculations use standard mathematical formulas and are verified for accuracy.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required — just open and use.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. All calculations run locally in your browser. Nothing is uploaded or stored.

Related Tools

Related Guides

Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Maintained and periodically reviewed by the YiJianSuan editorial team — review process in ourEditorial Policy.

Cite this page: YiJianSuan. Square Root Calculator[EB/OL]. https://www.yijiansuan.com/en/c/math/square-root

Results provided by this tool are for reference only and do not constitute professional advice.