About

In formal mathematics, leaving an answer as '√50' is often considered incomplete. The standard is to extract the largest perfect square, presenting the result as '5√2'. This process, known as simplifying radicals, is mandatory in Euclidean Geometry, Trigonometry, and Calculus.

This tool automates the prime factorization required to break down radicals. It handles operations between radicals, automatically grouping like terms (e.g., √2 + √8) by first simplifying them to a common base (√2 + 2√2 = 3√2).

Formulas

The simplifier uses the product rule for radicals:

√a × b = √a × √b

If 'a' is a perfect square (n²), it escapes the root:

√n²b = n√b

Reference Data

Radical	Simplified Form	Decimal Approx
√8	2√2	2.828
√12	2√3	3.464
√18	3√2	4.242
√20	2√5	4.472
√24	2√6	4.899
√27	3√3	5.196
√32	4√2	5.657
√45	3√5	6.708
√50	5√2	7.071
√75	5√3	8.660

Frequently Asked Questions

Like radicals have the same index and same radicand (the number inside). Only like radicals can be added or subtracted (e.g., 2√3 + 5√3 = 7√3).

Yes. √a × √b = √(a×b). The result can then be simplified. For example, √2 × √6 = √12 = 2√3.

Currently, this calculator specializes in Square Roots (index 2) as they are the most common in general education.

Decimals are approximations. 1.414 is close to √2, but if you square 1.414 you get 1.999396, not 2. Exact forms maintain precision.