What is the Value of the Square Root of 60?

As you should know from your high school algebra course, the square root y of a number x is such that y2 = x. By multiplying the value y by itself, we get the value x. For instance, 7.746 the square root of 60 because 7.7462 = 7.746×7.746 = 60.

Square root of 60 = 7.746

The square root of 60 is the number, which multiplied by itself 2 times, is 60. In other words, this number to the power of 2 equals 60.Besides the real values ofalong with an explanation, on this page you can also find what the elements of the square root of 60 are called.In addition to the terminology, we have a calculator you don’t want to miss:

Calculator

²√60 = ±7.7459666924This Square Root ⇄ Number Calculator is Really Cool! Click To Tweet If you have been looking for the square root of sixty, then you are right here, too.

Second Root of 60

In this section we provide you with important additional information about the topic of this post:The term can be written as ²√60 or 60^1/2.As the index 2 is even and 60 is greater than 0, 60 has two real square roots:²√60, which is positive and called principal square root of 60, and -²√60 which is negative.Together, they are denominated as Although the principal square root of sixty is only one of the two square roots, the term “square root of 60” usually refers to the positive number, that is the principal square root.

If you want to know how to find the value of this root, then read our article Square Root located in the header menu.

There, we also discuss the properties for index n = 2 by means of examples: multiplication, division, exponentiation etc.

Next, we have a look at the inverse function.

Inverse of Square Root of 60

Extracting the square root is the inverse operation of ^2:
In the following paragraph, we are going to name the elements of this √.

What is the Square Root of 60?

You already have the answer to that question, and you also know about the inverse operation of 60 square root.Keep reading to learn what the parts are called.

• ²√60 is the square root of 60 symbol
• 2 is the index
• 60 = radicand; the radicand is the number below the radical sign
• Square root = ±7.7459666924
• √ is called radical symbol or radical only

Second root of 60 = ±7.7459666924As a sidenote: All values on this page have been rounded to ten decimal places.Now you really know all about ²√60, including its values, parts and the inverse.If you need to extract the 2nd root of any other real number use our calculator above.Simply insert the number of which you want to find the square root (e.g. 60); the calculation is done automatically.

If you like our information about ²√60, then a similar square root you may be interested in is, for example: square root of 62.

In the following table you can find the n-th root of 60 for n = 2,3,4,5,6,7,8,9,10.

Table

The aim of this table is to provide you with an overview of the nth roots of 60.

IndexRadicandRootSymbolValue

2	60	Square Root of 60	²√60	±7.7459666924
3	60	Cube Root of 60	³√60	3.9148676412
4	60	Forth Root of 60	⁴√60	±2.7831576837
5	60	Fifth Root of 60	⁵√60	2.2679331553
6	60	Sixth Root of 60	⁶√60	±1.9786024465
7	60	Seventh Root of 60	⁷√60	1.7948229214
8	60	Eight Root of 60	⁸√60	±1.6682798577
9	60	Nineth Root of 60	⁹√60	1.5760586001
10	60	Tenth Root of 60	¹⁰√60	±1.5059658546

A few lines down from here we review the FAQs.

Square Root of Sixty

If you have been searching for what’s the square root of sixty or 2nd root of 60, then you are reading the right post as well.The same is true if you typed 2 root of 60 or 60 2 root in the search engine of your preference, just to name a few similar terms.

Right below you can find the frequently asked questions in the context.

FAQs About the Square Root of 60

Click on the question which is of interest to you to see the collapsible content answer.

60 has two real square roots, because the radicand 60 is positive and the index 2 is even.

The square root of 60 to the power of 2 equals 60.

Start with an initial guess such that 2 times that value equals approximately 60, then keep improving the guess until you have the required precision.

60 to the square root = 60^1/2 = ±7.7459666924.

The square root of 60 = ±7.7459666924.

To compute the 2nd root of 60 use a calculator, and/or employ the Newton–Raphson method.

The value of 2 root 60 is ±7.7459666924.

If something remains unclear do not hesitate getting in touch with us.We are constantly trying to improve our site, and truly appreciate your feedback.

Ahead is the wrap-up of our information.

Summary

To sum up, the square roots of 60 are ±7.7459666924; the positive real value is the principal.

Finding the second root of the number 60 is the inverse operation of rising the ²√60 to the power of 2. That is to say, (±7.7459666924)2 = 60.

Further information about the root of a number like ²√60 can be found on our page n-th Root.Note that you can also locate roots of real numbers such as ²√60 by means of the search form in the menu and in the sidebar of this site.If our article about the square √ 60 has been useful to you , then press some of the share buttons located at the bottom of this page.

BTW: A term closely related to square roots is perfect square. We tell you everything about perfect squares in our article Square Numbers.

If you have any questions about the 2nd root of 60, fill in the comment form below.Websites which are related to this one can be found in the “recommended sites” section in the sidebar.Last, but not least, don’t forget to install our absolutely free PWA app (see menu or sidebar), or to bookmark us.And come back soon!

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Here we will define, analyze, simplify, and calculate the square root of 60. We start off with the definition and then answer some common questions about the square root of 60. Then, we will show you different ways of calculating the square root of 60 with and without a computer or calculator. We have a lot of information to share, so let's get started!
Square root of 60 definition The square root of 60 in mathematical form is written with the radical sign like this √60. We call this the square root of 60 in radical form. The square root of 60 is a quantity (q) that when multiplied by itself will equal 60.

√60 = q × q = q2

Is 60 a perfect square? 60 is a perfect square if the square root of 60 equals a whole number. As we have calculated further down on this page, the square root of 60 is not a whole number. 60 is not a perfect square.
Is the square root of 60 rational or irrational? The square root of 60 is a rational number if 60 is a perfect square. It is an irrational number if it is not a perfect square. Since 60 is not a perfect square, it is an irrational number. This means that the answer to "the square root of 60?" will have an infinite number of decimals. The decimals will not terminate and you cannot make it into an exact fraction.

√60 is an irrational number

Can the square root of 60 be simplified? You can simplify 60 if you can make 60 inside the radical smaller. We call this process "to simplify a surd". The square root of 60 can be simplified.

√60 = 2√15

How to calculate the square root of 60 with a calculator The easiest and most boring way to calculate the square root of 60 is to use your calculator! Simply type in 60 followed by √x to get the answer. We did that with our calculator and got the following answer with 9 decimal numbers:

√60 ≈ 7.745966692

How to calculate the square root of 60 with a computer If you are using a computer that has Excel or Numbers, then you can enter SQRT(60) in a cell to get the square root of 60. Below is the result we got with 13 decimals. We call this the square root of 60 in decimal form.

SQRT(60) ≈ 7.7459666924148

What is the square root of 60 rounded? The square root of 60 rounded to the nearest tenth, means that you want one digit after the decimal point. The square root of 60 rounded to the nearest hundredth, means that you want two digits after the decimal point. The square root of 60 rounded to the nearest thousandth, means that you want three digits after the decimal point.

10th: √60 ≈ 7.7

100th: √60 ≈ 7.75

1000th: √60 ≈ 7.746

What is the square root of 60 as a fraction? Like we said above, since the square root of 60 is an irrational number, we cannot make it into an exact fraction. However, we can make it into an approximate fraction using the square root of 60 rounded to the nearest hundredth.

√60

≈ 7.75/1 ≈ 775/100

≈ 7 3/4

What is the square root of 60 written with an exponent? All square roots can be converted to a number (base) with a fractional exponent. The square root of 60 is no exception. Here is the rule and the answer to "the square root of 60 converted to a base with an exponent?":

√b = b½

√60 = 60½

How to find the square root of 60 by long division method Here we will show you how to calculate the square root of 60 using the long division method with one decimal place accuracy. This is the lost art of how they calculated the square root of 60 by hand before modern technology was invented.

Step 1)

Set up 60 in pairs of two digits from right to left and attach one set of 00 because we want one decimal:

Step 2) Starting with the first set: the largest perfect square less than or equal to 60 is 49, and the square root of 49 is 7. Therefore, put 7 on top and 49 at the bottom like this:

Step 3) Calculate 60 minus 49 and put the difference below. Then move down the next set of numbers.

Step 4) Double the number in green on top: 7 × 2 = 14. Then, use 14 and the bottom number to make this problem:

14? × ? ≤ 1100

The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 7. Now, enter 7 on top: That's it! The answer is on top. The square root of 60 with one digit decimal accuracy is 7.7.
Square Root of a Number Please enter another number in the box below to get the square root of the number and other detailed information like you got for 60 on this page.
Notes Remember that negative times negative equals positive. Thus, the square root of 60 does not only have the positive answer that we have explained above, but also the negative counterpart.

We often refer to perfect square roots on this page. You may want to use the list of perfect squares for reference.

Square Root of 61 Here is the next number on our list that we have equally detailed square root information about. Copyright  |   Privacy Policy  |   Disclaimer  |   Contact