Square Root Simplifier

How it is calculated

The input must be a whole number from 0 up to 9,007,199,254,740,991; a decimal such as 72.4 or a negative number shows no result. The tool strips the square factors of each prime in turn: if a prime p divides n an even number of times e, p^e/2 moves outside the root; if it divides an odd number of times, one copy stays inside. The product of what moved outside is the coefficient c, and √n = c × √r, where r is what remains under the radical. If r ends up as 1 only the whole number is shown (√49 gives 7); if c is 1 the root stays as √r. The decimal value is √n to three places. Zero returns 0.

Common mistakes

• Taking out a square that is not the largest. √72 = 2√18 is true but unfinished, since 18 still contains 9. The tool pulls out every square factor, giving 6√2.
• Entering a decimal such as 72.4 and expecting a decimal root. Only whole numbers are accepted and a decimal gives no result.
• Entering a negative number. There is no real square root, and the tool does not give an imaginary form such as i√8.
• Dropping the coefficient. 6√2 means 6 times √2, not √(6 × 2); entering 12 gives 2√3, which is a different number.
• Expecting a simplified form for every number. A number with no square factor, such as 17, stays √17, and only the decimal 4.123 helps there.