In this article we’re going to calculate the square root of 121 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 121 (both with and without a computer/calculator).

- Square Root of 121 Definition
- Is 121 a Perfect Square?
- Is The Square Root of 121 Rational or Irrational?
- Can the Square Root of 121 Be Simplified?
- How to Calculate The Square Root of 121 with a Calculator
- What is the Square Root of 121 Written with an Exponent?
- How to Find the Square Root of 121 Using Long Division
- Step 1
- Step 2
- Step 3
- Step 4
- Is a Perfect Square Root?
- The Prime Factors of 121 are
- How Do You Simplify the Square Root of 121 in Radical Form?

## Square Root of 121 Definition

In mathematical form we can show the square root of 121 using the radical sign, like this: √121. This is usually referred to as the square root of 121 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 121 is the quantity (which we will call q) that when multiplied by itself, will equal 121.

√121 = q × q = q2

## Is 121 a Perfect Square?

In math, we refer to 121 being a perfect square if the square root of 121 is a whole number.

In this case, as we will see in the calculations below, we can see that 121 is 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.

## Is The Square Root of 121 Rational or Irrational?

A common question is to ask whether the square root of 121 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 121 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 121 is a perfect square so we also can see that √121 is a rational number.

## Can the Square Root of 121 Be Simplified?

Since 121 is a perfect square it can be simplified because the result will always be equal to a whole number. Let’s simplify the square root of 121:

√121 = 11.

## How to Calculate The Square Root of 121 with a Calculator

On a computer you can also calculate the square root of 121 using Excel, Numbers, or Google Sheets and the SQRT function, like so:

SQRT(121) = 11

## What is the Square Root of 121 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 121:

√b = b½

√121 = 121½

## How to Find the Square Root of 121 Using Long Division

Finally, we can use the long division method to calculate the square root of 121. 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 121 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? × ? ≤ 21

The question marks are «blank» and the same «blank». With trial and error, we found the largest number «blank» can be is 1.

Now, enter 1 on top:

That’s it! The answer shown at the top in green. The square root of 121 with one digit decimal accuracy is 11.

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.

The symbol √ is calledradix, or radical sign

The number belowthe radix is the radicand

## Is a Perfect Square Root?

Yes. The square root of 121 is 11. Since 11 is a whole number, is a perfect square.

Previous perfect square root is: 100

Next perfect square root is: 144

## The Prime Factors of 121 are

11 × 11

## How Do You Simplify the Square Root of 121 in Radical Form?

= 11 × 11 = 11

Therefore, the answer is 11.

Since 121 is a perfect square (it’s square root will have no decimals), it is a rational number.