Maths Powers

Square root calculator

Number
Root
2 is a square root, 3 a cube root
Root 12
The 2th root of 144
Square root 12
Cube root 5.24148279
Whole number? yes
The original number 144
Note
Odd roots of negatives are real

The cube root of −27 is −3, because −3 × −3 × −3 gives −27. Any odd root of a negative number is real. Even roots are not: no real number squared gives −4, which is why the square root of a negative belongs to the complex numbers. This tool says so explicitly rather than returning a bare NaN.

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The square root of 144 is 12, because 12 × 12 = 144. The nth root of a number x is x raised to the power of 1/n. Odd roots of negative numbers are real — the cube root of −27 is −3 — but even roots of negatives are not.

How to find a root

1 Enter the number.
2 Set which root you want: 2 for square, 3 for cube, or any other.
3 Read the result, plus square and cube roots for comparison.
4 Check the note if the number is negative and the root is even.

A perfect square is one whose root is a whole number, and the first few are worth recognising on sight: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. Spotting them makes simplifying surds much faster — √72 becomes √36 × √2, which is 6√2. The tool flags whether a root came out whole for exactly that reason, since a non-whole result usually means the expression can be simplified rather than evaluated.

Questions

Twelve. It is a perfect square.

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