Turn Square Root Into Decimal Calculator

Square roots are fundamental in mathematics, but sometimes you need a decimal approximation for practical use. This calculator helps you convert square roots into decimal numbers quickly and accurately.

What is a square root?

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 × 3 = 9. Square roots are denoted by the radical symbol √.

Not all numbers have perfect square roots that are whole numbers. For example, √2 is approximately 1.41421356237. These are called irrational numbers and cannot be expressed as simple fractions.

How to convert square root to decimal

Converting a square root to a decimal involves finding an approximate value. Here are the main methods:

Use a calculator (most modern calculators have a √ button)
Use the long division method for manual calculation
Use the Newton-Raphson method for more precise results

For most practical purposes, decimal approximations to 5-10 decimal places are sufficient. More precise calculations are needed for scientific or engineering applications.

Manual calculation methods

Long division method

The long division method is a step-by-step process to find the decimal approximation of a square root:

Group the digits of the number in pairs from the decimal point
Find the largest number whose square is less than or equal to the first group
Subtract this square from the first group and bring down the next pair
Double the current result and find a digit to append that makes the new number closest to the next pair
Repeat the process until desired precision is achieved

Newton-Raphson method

This iterative method provides more precise results:

Start with an initial guess (often n/2)
Apply the formula: xₙ₊₁ = (xₙ + n/xₙ)/2
Repeat until the difference between consecutive terms is negligible

Common square roots

Here are some frequently encountered square roots and their decimal approximations:

Square Root	Decimal Approximation
√2	1.41421356237
√3	1.73205080757
√5	2.23606797750
√7	2.64575131106
√10	3.16227766017

FAQ

Why can't some square roots be expressed as exact decimals?

Some square roots, like √2, cannot be expressed as exact decimals because they are irrational numbers. They continue infinitely without repeating.

How many decimal places should I calculate for practical use?

For most everyday calculations, 4-5 decimal places are sufficient. More precise calculations are needed for scientific or engineering applications.

Is there a difference between square root and square?

Yes, the square of a number is that number multiplied by itself (e.g., 3² = 9), while the square root is the number that, when multiplied by itself, gives the original number (e.g., √9 = 3).