Here we will show you step-by-step how to simplify the square root of The square root of can be written as follows:
The symbol is called the radical sign. To simplify the square root of means to get simplest radical form of
Step 1: List Factors
List the factors of like so:
1, 5, 29,
Step 2: Find Perfect Squares
Identify the perfect squares*from the list of factors above:
Since 1 is the only perfect square above, the square root of cannot be simplified.
However, you may be interested in the decimal and exponent form instead.
Square root of in Decimal form rounded to nearest 5 decimals:
Square root of written with Exponent instead of Radical:
Simplify Square Root Calculator
Please enter another Square Root for us to simplify:
Simplify Square Root of
The answer to Simplify Square Root of is not the only problem we solved. Go here for the next problem on our list.
*List of Perfect Squares
Here we will define, analyze, simplify, and calculate the square root of We start off with the definition and then answer some common questions about the square root of Then, we will show you different ways of calculating the square root of with and without a computer or calculator. We have a lot of information to share, so let's get started!
Square root of definition
The square root of in mathematical form is written with the radical sign like this √ We call this the square root of in radical form. The square root of is a quantity (q) that when multiplied by itself will equal
√= q × q = q2
Is a perfect square?
is a perfect square if the square root of equals a whole number. As we have calculated further down on this page, the square root of is not a whole number.
is not a perfect square.
Is the square root of rational or irrational?
The square root of is a rational number if is a perfect square. It is an irrational number if it is not a perfect square. Since is not a perfect square, it is an irrational number. This means that the answer to "the square root of ?" will have an infinite number of decimals. The decimals will not terminate and you cannot make it into an exact fraction.
√is an irrational number
Can the square root of be simplified?
You can simplify if you can make inside the radical smaller. We call this process "to simplify a surd". The square root of cannot be simplified.
√is already in its simplest radical form.
How to calculate the square root of with a calculator
The easiest and most boring way to calculate the square root of is to use your calculator! Simply type in followed by √x to get the answer. We did that with our calculator and got the following answer with 9 decimal numbers:
How to calculate the square root of with a computer
If you are using a computer that has Excel or Numbers, then you can enter SQRT() in a cell to get the square root of Below is the result we got with 13 decimals. We call this the square root of in decimal form.
What is the square root of rounded?
The square root of rounded to the nearest tenth, means that you want one digit after the decimal point. The square root of rounded to the nearest hundredth, means that you want two digits after the decimal point. The square root of rounded to the nearest thousandth, means that you want three digits after the decimal point.
What is the square root of as a fraction?
Like we said above, since the square root of 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 rounded to the nearest hundredth.
≈ 12 1/25
What is the square root of written with an exponent?
All square roots can be converted to a number (base) with a fractional exponent. The square root of is no exception. Here is the rule and the answer to "the square root of converted to a base with an exponent?":
How to find the square root of by long division method
Here we will show you how to calculate the square root of using the long division method with one decimal place accuracy. This is the lost art of how they calculated the square root of by hand before modern technology was invented.
Set up in pairs of two digits from right to left and attach one set of 00 because we want one decimal:
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:
Calculate 1 minus 1 and put the difference below. Then move down the next set of numbers.
Double the number in green on top: 1 × 2 = 2. Then, use 2 and the bottom number to make this problem:
2?× ?≤ 45
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 =
Now, enter 2 on top, and 44 at the bottom:
Calculate 45 minus 44 and put the difference below. Then move down the next set of numbers.
Double the number in green on top: 12 × 2 = Then, use 24 and the bottom number to make this problem:
The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 0. Now, enter 0 on top:
That's it! The answer is on top. The square root of with one digit decimal accuracy is 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 on this page.
Remember that negative times negative equals positive. Thus, the square root of 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 squaresfor reference.
Square Root of
Here is the next number on our list that we have equally detailed square root information about.
What is the square root of in its simplest radical form? To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.
Unfortunately, the square root of cannot be simplified. Thus, here is the answer to the square root of in its simplest form:
√ = √
Here are two different methods we used to determine why the square root of cannot be simplified.
1) To be able to simplify the square root of , one of the factors of other than 1 must be a perfect square. The factors of are 1, 5, 29, and Since none of these factors are perfect squares, the square root of cannot be simplified.
2) To be able to simplify the square root of , all the prime factors of cannot be unique. When we did prime factorization of , we found that 5 x 29 equals Since all the prime factors are unique, the square root of cannot be simplified.
Simplify Square Root
Please enter another square root in the box below for us to simplify for you.
Simplify Square Root of
Here is the next square root on our list that we have simplifed.
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Root of 145 sqaure
Seeing Andrei, they politely greeted him, and in response to his dumb question, they said that they sometimes come here to his uncle Guram to help him. With the housework and to swim in the pool if he permits. Not paying attention to new acquaintances, Andrei went up to the room.
The room was empty, pouring water for himself, Andrei went out onto the balcony, there was no one by the pool either.Find positive square root of 6 145/256 - Question Number 4 - Part 3 - Exercise 2 - 8th Class Math
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