# Square Root of 5

The square root of 5 belongs to a long list of irrational algebraic numbers. It is classified in such a list because the square root of 5 cannot be expressed as a fraction and has an infinite number of decimals.

The square roots of 5 is usually written in mathematics as 5 and is called a positive algebraic number which when multiplied by itself gives the prime number 5. This is more accurately called the root square roots of 5, and is basically meant to differentiate itself from a negative number with the same property.

Like 2 and 3, the square roost of 5 also appears widely in formulas for exact trigonometric constants. It appears in many other examples as well. Geometrically, 5 is called a diagonal of a rectangle whose sides are of lengths 1 and 2. This is again prove by the Pythagorean theorem.

## What is the square root of 5?

The numerical value of the square root of 5, truncated to 50 decimal places, is as follows: 2.2360679774997896640917366873127623544061835961152… This is the simplified value of the square roots of 5. Interestingly, data from December 2013 shows that a numerical value of 5 has been calculate as a decimal number of at least ten billion digits.

#### How to find the square root of 5?

If you’re wondering how to find the square root of 5, the easiest way for you to do this is with the division method. In this method, you must first make an approximation, which means that you have found at least two square roots to find a close number that are perfect. This has to be the square root where your number falls in the middle. Then, you can divide the number by one of those square roots. Once you start and continue with the segmentation process, you need to take the result of Step 2 and the average of the original. And finally, you can use the result obtained in step 3. Repeat steps 2 and 3 until you find a number that is satisfactory or accurate to you. Example is given below:

Additionally, you can also try our square root calculator, which is an online tool that shows the square root for a given input. BYJU’S Square Root Calculator makes calculations easy and interesting. You just need to put the input as 5, and then the tool quickly shows the result for the given number.

Scroll to Top