POWERS & ROOTS

Find the square root of a number, plus its cube root and square. Enter a number.

Number

Square Root

—

Of the number.

Usage Tip

Estimate a square root by finding the two perfect squares it sits between — the root of 50 is between 7 (49) and 8 (64).

THE MATH

square root of x = the value that, squared, gives x
Also shown: cube root and the square

The square root reverses squaring. A perfect square (like 144) has a whole-number root.
Negative numbers have no real square root, but every number has a real cube root.

Only non-negative numbers have real square roots.
The cube root is defined for negatives too (cube root of -8 is -2).
A perfect square has an integer square root; most numbers do not.

Practical Notes

The square root of a number is the value that gives the number when multiplied by itself, so the square root of 49 is 7. The cube root works the same way with three factors, and the square simply multiplies the number by itself. These three operations come up constantly in geometry, physics, and statistics.

Numbers like 49 and 64 are perfect squares with whole number roots, while most roots, such as the square root of 2, are irrational and go on forever without repeating, so the calculator shows a rounded value. Only non-negative numbers have real square roots, but cube roots work for negative numbers as well, so the cube root of minus 27 is minus 3.

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