Complete step-by-step solution:
In the above question, we are given with whole number 2352
Now, finding the square root of this number,
We get,
$ \Rightarrow \sqrt {2352} = 48.497$
Now, the square root of the number $48.497$ . So, we can say that the number is not a perfect square.
Now, we have to find a smallest number which we can multiply to the number to make it a perfect square.
Firstly, we will do the factorization of the number 2352.
Now, the factor of 2352 is $2 \times 2 \times 2 \times 2 \times 3 \times 7 \times 7$ . Now, we know that the number can only be a perfect square when the factors of the number are in pairs.
So, from the factors of the number 2352, we can see that all the factors are in pairs, except factor 3.
So, we will multiply the number 2352 with 3 to make it a perfect square.
Now, to verify that 3 is the smallest number which is multiplied to 2352 to make it a perfect square, we need to multiply 3 with the number and then find its square root.
$ \Rightarrow 3 \times 2352 = 7056$
Now, finding the square root of the number $7056$ ,
We get,
$ \Rightarrow \sqrt {7056} = 84$
Hence, the number is a perfect square and the perfect square is 84.
Note: For a number to be called as a perfect square then the square root of that number should be the whole number. If the square root is not a whole number then it will be a terminating or non terminating decimal.
There are simple tricks or ideas to find out squares and square root easily
For example - if there is any number whose unit digit or at ones place there is 5 then its square or square root will contain 5 at its ones place .
It can be observed that 225 is square root of 15
Again , we know that 25 is a square of 5.
Here we will show you step-by-step how to simplify the square root of 2352. The square root of 2352 can be written as follows:
The √ symbol is called the radical sign. To simplify the square root of 2352 means to get the simplest radical form of √2352.
Step 1: List Factors
List the factors of 2352 like so:
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 49, 56, 84, 98, 112, 147, 168, 196, 294, 336, 392, 588, 784, 1176, 2352
We have 2352 = 2 × 2 × 2 × 2 × 3 × 7 × 7
As the prime factor 3 has no pair, 2352 is not a perfect square.
If 3 gets a pair then the number will become perfect square. So, we multiply 2352 by 3 to get,
2352 × 3 = 2 × 2 × 2 × 2 × 3 × 3 × 7 × 7
Now each prime factor is in a pair.
Therefore, 2352 × 3 = 7056 is a perfect square.
Thus the required smallest multiple of 2352 is 7056 which is a perfect square.
And, `sqrt[7056]` = 2 × 2 × 3 × 7 = 84.
IndexRadicandRootSymbolValue22352Square Root of 2352²√2352±48.497422611932352Cube Root of 2352³√235213.298799522342352Forth Root of 2352⁴√2352±6.964009090552352Fifth Root of 2352⁵√23524.723756075362352Sixth Root of 2352⁶√2352±3.64675191472352Seventh Root of 2352⁷√23523.031334780582352Eight Root of 2352⁸√2352±2.638940903292352Nineth Root of 2352⁹√23522.369213215102352Tenth Root of 2352¹⁰√2352±2.1734203632
A few lines down from here we review the FAQs.Square Root of Two Thousand Three Hundred Fifty-Two
If you have been searching for what’s the square root of two thousand three hundred fifty-two or 2nd root of 2352, then you are reading the right post as well.The same is true if you typed 2 root of 2352 or 2352 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 2352
Click on the question which is of interest to you to see the collapsible content answer.How Many Real Square Roots Does 2352 Have?
2352 has two real square roots, because the radicand 2352 is positive and the index 2 is even.
What to the Second Power Equals 2352?
The square root of 2352 to the power of 2 equals 2352.
How Do You Find the Square Root of 2352?
Start with an initial guess such that 2 times that value equals approximately 2352, then keep improving the guess until you have the required precision.
Here we will define, analyze, simplify, and calculate the square root of 2352. We start off with the definition and then answer some common questions about the square root of 2352. Then, we will show you different ways of calculating the square root of 2352 with and without a computer or calculator. We have a lot of information to share, so let's get started!
Square root of 2352 definition
The square root of 2352 in mathematical form is written with the radical sign like this √2352. We call this the square root of 2352 in radical form. The square root of 2352 is a quantity [q] that when multiplied by itself will equal 2352.
√2352 = q × q = q2
Is 2352 a perfect square?
2352 is a perfect square if the square root of 2352 equals a whole number. As we have calculated further down on this page, the square root of 2352 is not a whole number.
2352 is not a perfect square.
Is the square root of 2352 rational or irrational?
The square root of 2352 is a rational number if 2352 is a perfect square. It is an irrational number if it is not a perfect square. Since 2352 is not a perfect square, it is an irrational number. This means that the answer to "the square root of 2352?" will have an infinite number of decimals. The decimals will not terminate and you cannot make it into an exact fraction.
√2352 is an irrational number
Can the square root of 2352 be simplified?
You can simplify 2352 if you can make 2352 inside the radical smaller. We call this process "to simplify a surd". The square root of 2352 can be simplified.
√2352 = 28√3
How to calculate the square root of 2352 with a calculator
The easiest and most boring way to calculate the square root of 2352 is to use your calculator! Simply type in 2352 followed by √x to get the answer. We did that with our calculator and got the following answer with 9 decimal numbers:
√2352 ≈ 48.497422612
How to calculate the square root of 2352 with a computer
If you are using a computer that has Excel or Numbers, then you can enter SQRT[2352] in a cell to get the square root of 2352. Below is the result we got with 13 decimals. We call this the square root of 2352 in decimal form.
SQRT[2352] ≈ 48.4974226119286
What is the square root of 2352 rounded?
The square root of 2352 rounded to the nearest tenth, means that you want one digit after the decimal point. The square root of 2352 rounded to the nearest hundredth, means that you want two digits after the decimal point. The square root of 2352 rounded to the nearest thousandth, means that you want three digits after the decimal point.
10th: √2352 ≈ 48.5
100th: √2352 ≈ 48.50
1000th: √2352 ≈ 48.497
What is the square root of 2352 as a fraction?
Like we said above, since the square root of 2352 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 2352 rounded to the nearest hundredth.
√2352
≈ 48.50/1
≈ 4850/100
≈ 48 1/2
What is the square root of 2352 written with an exponent?
All square roots can be converted to a number [base] with a fractional exponent. The square root of 2352 is no exception. Here is the rule and the answer to "the square root of 2352 converted to a base with an exponent?":
√b = b½
√2352 = 2352½
How to find the square root of 2352 by long division method
Here we will show you how to calculate the square root of 2352 using the long division method with one decimal place accuracy. This is the lost art of how they calculated the square root of 2352 by hand before modern technology was invented.
Step 1]
Set up 2352 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 23 is 16, and the square root of 16 is 4. Therefore, put 4 on top and 16 at the bottom like this:
Step 3]
Calculate 23 minus 16 and put the difference below. Then move down the next set of numbers.
Step 4]
Double the number in green on top: 4 × 2 = 8. Then, use 8 and the bottom number to make this problem:
8? × ? ≤ 752
The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 8. Replace the question marks in the problem with 8 to get:
88 × 8 = 704.
Now, enter 8 on top, and 704 at the bottom:
Step 5]
Calculate 752 minus 704 and put the difference below. Then move down the next set of numbers.
Step 6]
Double the number in green on top: 48 × 2 = 96. Then, use 96 and the bottom number to make this problem:
96? × ? ≤ 4800
The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 4. Now, enter 4 on top:
That's it! The answer is on top. The square root of 2352 with one digit decimal accuracy is 48.4. Did you notice that the last two steps repeat the previous two steps. You can add decimals by simply adding more sets of 00 and repeating the last two steps over and over.
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 2352 on this page.
Notes
Remember that negative times negative equals positive. Thus, the square root of 2352 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.