Square Root Calculator

How to use

1. 1Enter a number and a root index (2 for square root, 3 for cube root, up to 100).
2. 2Read the simplified radical plus the decimal square, cube and nth roots.
3. 3Use the exponent section for aᵇ — whole-number powers are calculated exactly.
4. 4Convert any number to or from scientific notation in the last section.

Simplifying square roots

To simplify √72, factor the number into primes — 72 = 2³ × 3² — and take out every pair: one pair of 2s and one pair of 3s come out as 2 × 3 = 6, and a single 2 stays inside, so √72 = 6√2. For nth roots, groups of n equal factors move outside: ∛54 = 3∛2 because 54 = 3³ × 2. Perfect powers simplify completely (√144 = 12, labelled “Exact root”), while numbers without repeated factors, such as √30, cannot be simplified.

Roots of negative numbers and decimals

Odd roots of negative numbers are real: ∛−27 = −3. Even roots of negative numbers have no real value — √−16 is the imaginary number 4i — so the calculator shows “No real root” instead of a complex result. Decimal inputs work for the decimal roots (√2.25 = 1.5); radical simplification applies to whole numbers. Very large or very small results switch to scientific notation automatically.

Exact powers and scientific notation

When both the base and the exponent are whole numbers, aᵇ is calculated with BigInt, so 2⁶⁴ shows all 20 digits (18446744073709551616) instead of a rounded floating-point value, together with the digit count and scientific notation. Negative exponents give a fraction (2⁻³ = 1/8 = 0.125), and decimal bases or exponents use standard floating-point math. The scientific-notation converter turns 0.000123 into 1.23 × 10⁻⁴ (E notation 1.23E-4) and back, and accepts inputs such as 6.02e23.

Frequently asked questions

Related tools