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Square root calculator

Compute the square root of a number, plus its square.

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Need Square root, Square (n²)? The Square root calculator derives it from Number in one step. For instance, with Number = 144 it returns Square root = 12 and Square (n²) = 20,736.

How to use it

  1. Enter your values: Number.
  2. Read the result instantly: Square root, Square (n²).

Frequently asked questions

What does the Square root calculator actually compute?

It takes Number and derives Square root and Square (n²) from them. The calculation is live as you type, so the result updates on every change.

What information do I need to provide?

A single value: Number. Nothing else is required — no account, no file upload.

Can you show a worked example?

With Number = 144, the calculator returns Square root = 12 and Square (n²) = 20,736. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

What happens if I enter larger values?

It moves a lot. Using Number = 288 instead, Square root goes from 12 to 16.971 — which is why it is worth testing a few scenarios rather than trusting a single figure.

What does it give for smaller values?

Scaled down to Number = 72, Square root comes out at 8.485. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Getting through a problem set: solving for the unknown, factoring an expression, and — more usefully — seeing the steps that got there.

What is the most common mistake?

Losing a solution when both sides are squared or divided by an expression. Squaring can add roots that do not satisfy the original equation, and dividing can remove one — check every answer back in the original.

What is the difference between the Square root calculator and the Cube root calculator?

This one returns Square root and Square (n²); the Cube root calculator returns Cube root and Cube (n³). That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Nth root calculator is the closest one after this: Compute any root (square, cube, nth) of a number.

What else is worth having open alongside it?

Primitive root calculator and Root Mean Square Calculator — they come up in the same task often enough to be worth a second tab.

Further reading

All guides →
How-toHow to Find a Cube Root by HandA step-by-step guide to finding a cube root by estimation and refinement — plus how it differs from a square root and when a value stays irrational.ExplainerHow Exponents Work: Powers and the Laws of ExponentsAn exponent is repeated multiplication. Learn the laws of exponents, what negative and fractional powers mean, and why anything to the zero is one.How-toHow to Find the Area of a Triangle: Base × Height and Heron's FormulaTwo reliable ways to find a triangle's area: half base times height when you know the height, and Heron's formula when you only know the three sides.How-toHow to Use the Quadratic Formula: Solving ax² + bx + c = 0Solve any quadratic equation with x = (−b ± √(b² − 4ac)) / 2a, and read the discriminant to know how many real solutions to expect.How-toHow to Calculate the Square Metres of a RoomFind a room's area by multiplying length by width. Here's the method for rectangular, L-shaped and round rooms, and why area drives your material orders.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.