What is the Square Root of 108?

The symbol √ is calledradix, or radical sign

The number belowthe radix is the radicand

In this article we will look at the cube root of the number 108 and show you how to calculate it and determine if it is a perfect cube or not.

Square root =

(Results rounded to nearest 0.0001)

How much is the square root of 108?

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More Square Roots Starting with 108

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In this article we’re going to calculate the square root of 108 and explore what the square root is and answer some of the common questions you might. We’ll also look at the different methods for calculating the square root of 108 (both with and without a computer/calculator).

What is 108 square root simplified?, The square root of 108 is simplified as 6√3.

Furthermore, What is the perfect square of 108?, We determined above that the greatest perfect square from the list of all factors of 108 is 36.

Finally,  IS 108 a perfect square root?, 108 is not a perfect square.

Frequently Asked Question

Is 108 a Perfect Cube? The number 108 on prime factorization gives 2 × 2 × 3 × 3 × 3. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 108 is irrational, hence 108 is not a perfect cube.

What is a perfect square root?

Factors of 108: 1, 2, 3 , 4, 6, 9, 12, 18, 27, 36, 54, and 108.

IS 108 is a perfect cube?

Simplifying a square root just means factoring out any perfect squares from the radicand, moving them to the left of the radical symbol, and leaving the other factor inside the radical symbol. If the number is a perfect square, then the radical sign will disappear once you write down its root.

What square roots Cannot be simplified?

This allowed us to take the square root of the perfect square (which results in a whole number) and then we must leave the square root of 2, as the square root of 2 because it cannot be simplified any further.

What is a square root for dummies?

A square root of a number is a value that, when multiplied by itself, gives the number. Example: 4 × 4 = 16, so a square root of 16 is 4.

What is the square root of 108 in radical form?

Whenever the cube root of a given number is a whole number without any fractional or decimal part, we call this a perfect cube.

These are important for a lot of different math functions and can be used in simpler settings like carpenty and room design all the way through to more advanced calculations in physics and astronomy.

For the number 108 we have already calculated the answer of 4.7622031559046 using a scientific calculator and since this is not a whole number, we also know that 108 is not a perfect cube number.

We have a list of perfect cubes article which covers the first 500 perfect cube numbers for you.

Calculate a cube root problem

If you have an example you want to try and see if it is a perfect cube, enter it in the form below and click calculate to find out if it is.

Enter your number in box A below and click «Calculate» to work out the cube root of the given number.

Practice perfect cube and cube roots using examples

Still here and interested in perfect cubes? You must really love yourself some math!

Take a look at the random calculations in the sidebar on the right hand side of this page and click through to some of the cube root calculations.

How many of them are perfect cubes? You can also try to think of and calculate some perfect cubes yourself without looking at the list above to test yourself.

Can the Square Root of 108 Be Simplified?

108 can be simplified only if you can make 108 inside the radical symbol smaller. This is a process that is called simplifying the surd. In this example, the square root of 108 can be simplified.

√108 = 6√3.

Simplifying the cube root of 108

Sometimes, the radicand can be simplified and made smaller. If that is possible, we call it the cube root of 108 in its simplest form.

In our example, the cube root of 108 can be simplified and expressed in its simplest form:

∛108 = 3∛1

What is the Square Root of 108 as a Fraction?

We covered earlier in this article that only a rational number can be written as a fraction, and irrational numbers cannot.

Like we said above, since the square root of 108 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 108 rounded to the nearest hundredth.

≈ 10 39/100

How to Calculate The Square Root of 108 with a Calculator

√108 ≈ 10.3923

The Prime Factors of 108 are

Since 108 isn’t a perfect square (it’s square root will have an infinite number of decimals), it is an irrational number.

Is the cube root of 108 a rational or irrational number?

This is a commonly asked question and the answer to whether the cube root of 108 is rational or irrational is always the same as if it is a perfect cube.

Remember that a rational number can be written as a fraction, while irrational numbers can’t.

So, if a number is a perfect cube, then it’s a rational number, but if it is not a perfect cube then it is an irrational number.

We just confirmed that 108 is not a rational number then, because we know it is not a perfect cube number.

What is a cube root?

The cube root of 108 is another number that when multiplied by itself twice, would be exactly equal to 108.

We would normally express this problem in mathematical form by using the cube root symbol with the number alongside it:

You might notice that this symbol is very similar to the square root symbol. The only difference is the number, called the index, above the symbol, which lets us know this a cube root calculation.

To recap: the √ symbol itself is called the radical symbol, the number above it is called the index, and the actual number, 108, is called the radicand.

The basic formula we use to calculate a cube number from the result is a number which we’ll call n in this example, that when multiplied by itself twice, is equal to 108:

n × n × n = 108

When we use ∛108, the actual math calculation we perform is 108⅓. This means you can use that formula in Excel, Google Sheets, or Mac Numbers to calculate the cube root:

You should now be able to confirm that the cube root of 108 is:

∛108 ≈ 4.7622031559046

How to Find the Square Root of 108 Using Long Division

Finally, we can use the long division method to calculate the square root of 108. This is very useful for long division test problems and was how mathematicians would calculate the square root of a number before calculators and computers were invented.

Step 1

Set up 108 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 1 is 1, and the square root of 1 is 1 . Therefore, put 1 on top and 1 at the bottom like this:

Step 3

Calculate 1 minus 1 and put the difference below. Then move down the next set of numbers.

Step 4

Double the number in green on top: 1 × 2 = 2. Then, use 2 and the bottom number to make this problem:

2? × ? ≤ 8

The question marks are «blank» and the same «blank». With trial and error, we found the largest number «blank» can be is 0. Replace the question marks in the problem with 0 to get:

20 × 0 = 0

Now, enter 0 on top, and 0 at the bottom:

Step 5

Calculate 8 minus 0 and put the difference below. Then move down the next set of numbers.

Step 6

Double the number in green on top: 10 × 2 = 20. Then, use 20 and the bottom number to make this problem:

20? × ? ≤ 800

The question marks are «blank» and the same «blank». With trial and error, we found the largest number «blank» can be is 3.

Now, enter 3 on top:

That’s it! The answer shown at the top in green. The square root of 108 with one digit decimal accuracy is 10.4.
Notice that the last two steps actually repeat the previous two. To add decimal places to your answe you can simply add more sets of 00 and repeat the last two steps.

Rounding the cube root of 108

There might be occasions when you need to round the result of a cube root calculation down to a specific number of decimal places. Below, we show an example of a few of these to specific decimal places that show up in exam questions:

10th: ∛108 = 4.8

100th: ∛108 = 4.76

1000th: ∛108 = 4.762

How Do You Simplify the Square Root of 108 in Radical Form?

= 2 × 2 × 3 × 3 × 3 = 6

Therefore, the answer is 6.

Is 108 a Perfect Square?

In math, we refer to 108 being a perfect square if the square root of 108 is a whole number.

In this case, as we will see in the calculations below, we can see that 108 is not a perfect square.

To find out more about perfect squares, you can read about them and look at a list of 1000 of them in our What is a Perfect Square? article.

A common question is to ask whether the square root of 108 is rational or irrational. Rational numbers can be written as a fraction and irrational numbers cannot.

A quick way to check this is to see if 108 is a perfect square. If it is, then it is a rational number. If it’s not a perfect square then it’s an irrational number.

We already know if 108 is a perfect square so we also can see that √108 is an irrational number.

What is the Square Root of 108 Rounded?

Sometimes you might need to round the square root of 108 down to a certain number of decimal places. Here are the solutions to that, if needed.

10th: √108 ≈ 10.4

100th: √108 ≈ 10.39

1000th: √108 ≈ 10.392

How to Calculate the Square Root of 108 with a Computer

On a computer you can also calculate the square root of 108 using Excel, Numbers, or Google Sheets and the SQRT function, like so:

SQRT(108) ≈ 10.392304845413

What is the Square Root of 108 Written with an Exponent?

All square root calculations can be converted to a number (called the base) with a fractional exponent. Let’s see how to do that with the square root of 108:

√b = b½

√108 = 108½

Is a Perfect Square Root?

No. The square root of 108 is not an integer, hence √108 isn’t a perfect square.

Previous perfect square root is: 100

Next perfect square root is: 121

Square Root of 108 Definition

In mathematical form we can show the square root of 108 using the radical sign, like this: √108. This is usually referred to as the square root of 108 in radical form.

Want to quickly learn or refresh memory on how to calculate square root play this quick and informative video now!

So what is the square root? In this case, the square root of 108 is the quantity (which we will call q) that when multiplied by itself, will equal 108.

√108 = q × q = q2