Square Root Calculator and Radical Simplifier
By Hesaplayıcı
The square root calculator finds the square root of the number you enter. For a whole number it also simplifies the root to a√b: a is the coefficient taken out of the root and b is the number left under it. Enter the number and press Calculate. Negative numbers have no real square root.
Worked example: Square root of 72
Square root
8.49
- Coefficient outside the root (a)
- 6
- Number under the root (b)
- 2
Step by step
Square root
root = √x
root = √72 = 8.49
√x = a × √b, a² × b = x
√72 = √(6² × 2) = 6 × √2 = 8.49
How to use
- Enter the Number. It must be 0 or more.
- Press Calculate. You get the square root and, for a whole number, the simplified radical.
Formula
√x = a × √b, where a² × b = x.
x is the number you enter. a is the largest whole number whose square divides x. b is x divided by a², and it has no square factor left. For example, √50 = √(25 × 2) = 5 × √2. When the number is a perfect square, b = 1 and the square root is a whole number.
Worked example
The worked example on this page takes the square root of 72 and simplifies it. The first step gives the square root; the second gives the coefficient taken out of the root and the number left under it.
Limits
The calculator computes square roots only, not cube or other roots. It gives no complex roots of negative numbers. Decimals are not simplified. The square root is accurate to about 16 significant digits; the page may shorten it. The number can be at most 10¹².
Frequently Asked Questions
What is a square root?
The square root of a number is the non-negative number whose square is that number. For example, 14² = 196, so √196 = 14.
How do you simplify a square root?
Write the number under the root as a perfect square times another number, then take the root of the perfect square out. For example, √50 = √(25 × 2) = 5√2.
Does a negative number have a square root?
Not among the real numbers, because no real number has a negative square. The square roots of negative numbers are complex numbers, which the calculator does not compute.
Can I take the square root of a decimal?
Yes. The calculator gives the square root of a decimal, but it does not simplify it to a√b.
Calculation rules
- The square root is the non-negative number whose square is the given number. Negative numbers have no real square root; the calculator accepts 0 and above.
- For whole numbers the root is written as a√b: a is the largest whole number whose square divides the number, and b has no square factor left. Decimals are not simplified.
- The square root is not rounded; it is accurate to about 16 significant digits (double precision). The page may shorten numbers.