Is square root of 144 a rational number

Q: Is 144 square a rational number?

Answer and Explanation: The number 144 squared is a rational number. When you square 144, you multiply 144 by itself: 144 x 144. This equals 20,736.

There are six common sets of numbers.

Table of Contents Show

Simplification of Square Root of 144
Is 144 rational or irrational number?
Why is the square root of 144 a rational number?
Is 144 square a rational number?
Is root 144 a real number?

Natural (Counting) Numbers:

Whole Numbers: Natural Numbers and

Rational Numbers: Integers, Fractions, and Terminating or Repeating Decimals

Irrational Numbers: Non Terminating or Non Repeating Decimals

Real Numbers: Rational Numbers and Irrational Numbers

The value of the square root of 144 is equal to 12. In radical form, it is denoted as √144 = 12. To calculate the value to root 144 without using a calculator, there are two methods: one is the prime factorisation and another is the long division method. We will learn both the methods here, which will help students to find the root of any number easily and in the fastest way. Also, learn here about square root in a detailed way.

Square root of 144, √144 = 12

As per the given expression above, we can define the square root of natural number 144, is a value which on multiplying by itself gives 144.

Hence, 12 x 12 = 144 or 122 = 144

Simplification of Square Root of 144

Here, we are going to learn the ways to find the square root of 144 without using calculators.

Prime Factorisation:

In prime factorisation, we have to find the prime factors in the given number. This method is easy to apply, as we have learned about prime factors in our earlier classes. But, it can only be used if a number is a perfect square.

Clearly, 144 is a perfect square, thus the prime factors are,

144 = 2x2x2x2x3x3

Therefore, if we take the square root on both the sides, we get;

√144 = √(2x2x2x2x3x3)

As we can see here, there are two pairs of 2 and one pair of 3. Hence,

√144 = 2x2x3

√144 = 12

Long Division method

We can also find the square root of any number using long division method. This method is very useful and is the fastest method of all to find the root. It can be used to find the root of imperfect squares and of large numbers, which is not possible in the case of prime factorisation. Below are the steps for using the long division method.

Here we will define, analyze, simplify, and calculate the square root of 144. We start off with the definition and then answer some common questions about the square root of 144. Then, we will show you different ways of calculating the square root of 144 with and without a computer or calculator. We have a lot of information to share, so let's get started!

Square root of 144 definition
The square root of 144 in mathematical form is written with the radical sign like this √144. We call this the square root of 144 in radical form. The square root of 144 is a quantity (q) that when multiplied by itself will equal 144.

√144 = q × q = q2

Is 144 a perfect square?
144 is a perfect square if the square root of 144 equals a whole number. As we have calculated further down on this page, the square root of 144 is a whole number.

144 is a perfect square.

Is the square root of 144 rational or irrational?
The square root of 144 is a rational number if 144 is a perfect square. It is an irrational number if it is not a perfect square. Since 144 is a perfect square, it is rational number. This means that the answer to "the square root of 144?" will have no decimals.

√144 is a rational number

Can the square root of 144 be simplified?
A square root of a perfect square can be simplified because the square root of a perfect square will equal a whole number:

√144 = 12

How to calculate the square root of 144 with a calculator
The easiest and most boring way to calculate the square root of 144 is to use your calculator! Simply type in 144 followed by √x to get the answer. We did that with our calculator and got the following answer:

√144 = 12

How to calculate the square root of 144 with a computer
If you are using a computer that has Excel or Numbers, then you can enter SQRT(144) in a cell to get the square root of 144. Below is the result we got:

SQRT(144) = 12

What is the square root of 144 written with an exponent?
All square roots can be converted to a number (base) with a fractional exponent. The square root of 144 is no exception. Here is the rule and the answer to "the square root of 144 converted to a base with an exponent?":

√b = b½

√144 = 144½

How to find the square root of 144 by long division method
Here we will show you how to calculate the square root of 144 using the long division method. This is the lost art of how they calculated the square root of 144 by hand before modern technology was invented.

Step 1)
Set up 144 in pairs of two digits from right to left:

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? × ? ≤ 44

The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 2. Replace the question marks in the problem with 2 to get:

22 × 2 = 44.

Now, enter 2 on top, and 44 at the bottom:

The difference between the bottom two numbers is zero, therefore, you are done! The answer is the green numbers on top. Once again, the square root of 144 is 12.

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 144 on this page.

Notes
Remember that negative times negative equals positive. Thus, the square root of 144 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.

Is 144 rational or irrational number?

The number 144 is a rational number. A rational number is defined as any number that can be written as a ratio, or fraction, between two integers. Like all whole numbers, 144 can be written as a fraction with a denominator of 1, as in 144/1. Since both 144 and 1 are both integers, we know that 144 is a rational number.

Why is the square root of 144 a rational number?

Answer and Explanation: The number 144 is a perfect square. This means that its square root is a whole number, or integer. The number 144 is the product of the integer 12 multiplied by itself (12 x 12). By definition, the square root of all perfect squares are rational numbers.

Is 144 square a rational number?

Answer and Explanation: The number '144 squared' is a rational number. When you square 144, you multiply 144 by itself: 144 x 144. This equals 20,736.