Square Root Calculator

In the wise words of Yoda "Peculiar numbers, square roots are". A square root is the value of a number that multiplies by itself to give a particular number. For example, the square root of 4 is 2 because multiplying 2 by itself gives you 4.

  1. Simply enter a number to calculate the square root.
Square Root Calculator
Square Root Results
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Square Root Calculator. This image shows the properties and Square Root formula for the Square Root Calculator

How to use the Square Root Calculator

Simply enter a number to calculate the square root of the number entered.

A Square Root Calculator to Uproot Your Calculation Problems

If you are given a*a = x, then a is the square root of x and x is the square of a.

Mathematically,

a*a = x
a² = x
a = √x

Properties of Square Root

Just the way exponential functions have their own set of properties, square root functions have the following essential properties:

Product property of square roots

For a set of numbers, the product of square roots is equal to the square root of the product of the numbers.

√a * √b = √(a*b)
√4 * √9 = √(4*9)
2 * 3 = √(36)
6 = 6

Quotient property of square roots

For a set of numbers, the fraction of the square root of two numbers is equal to the square root of the fractions.

√a / √b = √(a/b)

Where b must be a non-zero number.

√36 / √9 = √(36/9)
6/3 = √(4)
2 =2

Other properties of square roots are:

  • The square root of an odd number will be an odd number (√625 = 25, an odd number)
  • Similarly, the square root of an even number will be an even number. (√196 = 14, an even number)
  • Numbers ending with an odd number of zeros are not perfect squares. For example, 100, 400, 900 have 10, 20, and 30 as square roots, and thus, are perfect squares. However, 1000, 4000, and 9000 do not have a perfect square root.
  • Starting from 1, the sum of the first n odd numbers is n². For example, add the first 13 odd numbers, 1+3+5+7+9+11+13+15+17+19+21+23+25. The sum of these numbers equals 169, which is the square of 13. Try it with any number of odd numbers, just start from 1 and keep on adding as many consecutive odd numbers as you want.
  • There are no square roots of negative numbers in the rational number system. This is where the concept of iota comes into the picture, but that's beyond the scope of this article.

How to Calculate the Square Root of a Number

While there are many ways to calculate the square root of a number, we will look at the simplest of them all:

By using prime factorization

This method is primarily used for large numbers that can be factorized into perfect square factors. For example, consider the number given below:

√196

Start with finding the perfect square factors, you'll have:

√196 = √(49 x 4)

Now, take the square roots of the perfect square factors:

√196 = √(7² x 2²)
√196 = √7² x √2²
√196 = 7 x 2
√196 = 14

This method is useful only when you are expert in finding perfect square factors for a given number. And this particular task in itself is quite daunting.

The other methods of finding perfect squares are more time consuming than this one. And they all are error-prone if you are not careful. This is why iCalculator developed an extremely easy to use square root calculator. The best part of this online calculator is that it also works wonderfully well for finding the square root of non-perfect square numbers.

How to Use the Square Root Calculator

All you need to do is simply open the link to the square root calculator and enter the number you want to find the square root of. That's it. This extremely easy to use math calculator requires nothing else from you. Just give it a positive number and it will give you its square root instantly.

Use of Square Roots in Real Life

Engineers, architects, and carpenters are among those professionals that calculate square roots on a daily basis. At the same time, square roots are also used as mental exercises for developing logical thinking.

Square roots are also critical in probability and statistics to find the standard deviation.

Summary

Surprisingly, the number (1 + √5)/2 is a number that determines how a tree's branches are distributed across the trees to help leaves absorb the maximum amount of sunlight. The same number also determines how the seeds of a sunflower are packed on its face. Unusual, right? Well, that's the beauty of math. It's everywhere, you just need to be observant enough.

From construction to algebra to nature, square roots play an important role in all walks of life. However, their importance doesn't mean that finding square roots has to be a time consuming and mind-boggling task. Just enter a positive number in square root calculator developed by iCalculator, and get accurate results instantly.

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