Reviewed by David Chen, CFA
Understanding how to square root on a calculator is a fundamental skill for algebra, finance, and engineering. Use our professional tool below to find the square root of any positive number instantly, with a detailed breakdown of the calculation steps.
How to Square Root on a Calculator
Square Root Formula:
Source: Khan Academy – Radicals, Math Is Fun
Variables:
- Number (x): The value (radicand) you want to find the square root of.
- Square Root (r): A value that, when multiplied by itself, gives the original number.
- Radical Symbol ($\sqrt{\quad}$): The symbol used to denote the principal square root.
What is a Square Root?
A square root of a number $x$ is a number $r$ such that $r^2 = x$. For example, 4 and -4 are square roots of 16 because $4^2 = 16$ and $(-4)^2 = 16$. However, when people ask how to square root on a calculator, they are typically looking for the “principal” (positive) square root.
Calculators use iterative algorithms, such as the Babylonian method or Newton’s method, to provide high-precision approximations for irrational numbers like $\sqrt{2}$ or $\sqrt{3}$, which cannot be expressed as simple fractions.
How to Calculate Square Root (Example):
- Identify the number you want to solve (e.g., $x = 25$).
- Estimate the root: Since $4^2=16$ and $5^2=25$, the answer is exactly 5.
- For non-perfect squares like 20, find the two closest perfect squares (16 and 25). The root is between 4 and 5.
- On a physical calculator, press the $\sqrt{\quad}$ button first, then the number, followed by “=”.
Related Calculators:
Frequently Asked Questions (FAQ):
Can you find the square root of a negative number?
In the real number system, no. However, in mathematics, the square root of a negative number is represented as an “imaginary number” using the symbol $i$ (where $i = \sqrt{-1}$).
What is the difference between $\sqrt{x}$ and $x^2$?
They are inverse operations. Squaring a number ($x^2$) means multiplying it by itself. Taking the square root ($\sqrt{x}$) finds the original factor that was squared.
Why does my calculator show an error for $\sqrt{-4}$?
Most standard calculators are set to work with Real Numbers only. Since no real number multiplied by itself equals a negative, the calculator returns an error.
How do I find a square root without a calculator?
You can use the “Long Division Method” for square roots or the “Prime Factorization Method” for perfect squares.