√ Square Root & Exponent Calculator
Calculate roots and powers of any number
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Roots & Exponents Guide
What Is a Square Root?
The square root of a number x is the value that, multiplied by itself, gives x. For example, the square root of 16 is 4, because 4 × 4 = 16. The cube root of a number is the value that, multiplied by itself three times, gives that number — the cube root of 27 is 3, since 3 × 3 × 3 = 27.
What Is an Exponent?
An exponent tells you how many times to multiply a base number by itself. 2³ (2 to the power of 3) means 2 × 2 × 2 = 8. Exponents can also be negative (2⁻¹ = 1/2 = 0.5) or fractional (x^0.5 is the same as the square root of x).
| Expression | Meaning | Example |
|---|---|---|
| x² | x squared | 5² = 25 |
| x³ | x cubed | 5³ = 125 |
| x^0.5 | Square root of x | 25^0.5 = 5 |
| x⁻¹ | Reciprocal of x | 5⁻¹ = 0.2 |
| x⁰ | Always equals 1 (x ≠ 0) | 5⁰ = 1 |
Frequently Asked Questions
Can you take the square root of a negative number?
Not as a real number — the square root of a negative number is what's called an "imaginary" number (involving i, the square root of -1). This calculator will flag that as invalid, since it works with real numbers only.
Can you take the cube root of a negative number?
Yes — unlike square roots, odd-numbered roots (cube root, 5th root, etc.) of negative numbers ARE real. For example, the cube root of -8 is -2, because -2 × -2 × -2 = -8.
What does a negative exponent mean?
A negative exponent means "take the reciprocal." For example, 2⁻³ = 1/(2³) = 1/8 = 0.125. It does NOT mean the result is negative.
What is x to the power of 0?
Any nonzero number raised to the power of 0 equals 1. This might seem surprising, but it follows from the pattern of dividing successive powers (x³/x² = x, x²/x¹ = x, x¹/x⁰ = x, which only works if x⁰ = 1).
How is a fractional exponent related to roots?
x^(1/n) is the same as the nth root of x. So x^0.5 is the square root, x^(1/3) is the cube root, and so on. This calculator's Power mode lets you verify this directly using the 0.5 exponent preset.