The square root is an operation in which if you take a number and perform the operation would give you the same result as when you multiply it by itself. Square roots take the form \[\sqrt{x}\] wherein x is the number you are executing the operation on. For a number which is non-negative and real, denoted as n, for example, 8, the principal square root refers to the non-negative result of x2 = n.
The square root of 8, denoted by \[\sqrt{8}\], is the number whose square gives you the number 8. In a simpler for, \[\sqrt{8}\] is written as \[2\sqrt{2}\]. This value is called surd since you cannot simplify this further. However, 8 is a perfect cube of the number 2 since 2 x 2 x 2 = 8. So, you can easily find the cube root of 8 which is denoted as \[\sqrt[3]{8}\]= 2. However, there are a few numbers like 4, 9, 16, etc. that are perfect squares and whose squares are easy to find. In this article, we will learn about the square root of 8 and how to find the root 8 value.
\[\sqrt{4}\] = 2, as you know 2 x 2 = 4
\[\sqrt{9}\] = 3, as you know 3 x 3 = 9
\[\sqrt{16}\] = 4, as you know 4 x 4 = 16
Any square root is represented by the square root symbol √. This symbol is known as the radical symbol or simply radix. The number underneath this radical symbol is known as radicand. Hence, the number whose square root is to be determined is called the radicand.
The value of root 8 is \[\sqrt{8}\] = 2.82842712475
If you consider the first three decimal places \[\sqrt{8}\] = 2.828
Now, since you know the value of root 8, let us find out how to calculate its value here. Although it is easy to find the root 8 value by using a calculator, you should know how to find its value manually.
The square root of a number is represented by the symbol √. This symbol is known as the radical symbol or radix. The number underneath this radix is called as radicand.
Let us estimate the value of the square roots now.
Estimating square roots depends on what you use. suppose you need to find the square root of number denoted by x.
To simplify your answer for finding the square root roughly, consider finding two other numbers n and m in such a way that n2 <x<m2. When you have this relationship between all these three numbers, it would be sure to say that √x is a number which lies in between the numbers n and m.
For example, if you have to find the square root of the number 40, denoted as √40, you can easily say that the answer to the root 40 lies in between the numbers 6 and 7. You can use this method with rational numbers as well. Consider this example and by performing a few calculations you can actually figure out that the root of 40 lies in between the numbers 6.3 and 6.4.
The other way to find the square root of a number is by factoring the number x with the prime numbers and then simplifying the squared numbers if there are any. This way you would be left with just the smaller roots for the calculation.
Suppose you have to find the value of √18. You can write the number 18 as 2 x 32. Therefore, \[\sqrt{18}\] = \[\sqrt{2}\] x \[\sqrt{3^{2}}\]. Further, when you simplify this, you get 3\[\sqrt{2}\].
For you to remember, 22= 4, and 32= 9. Hence the answer to the root of 8 lies between the numbers 2 and 3. However, since the square of 3 equals to 9 which is larger than 8, the root 8 value lies in between the number 2.8 and 2.9.
The precise answer of the square root of 8 is 2.82842712475. this is much closer to the answer that we estimated.
Well, did you know the answer to the square root of 8 to the power 3? For solving this, you need to first find out the root 8 value. Then multiply this value by itself for 3 times to get the answer.
Therefore, the answer to the square root of 8 to power 3 is (2.828) x 3 = 22.627.
Do you know what the square root of 8 to the power of 3 is? To solve the problem, we need to take the square root of 8. Then, we take that value and multiply by itself 3 times.
So essentially, square root of 8 to the power of 3 = (2.828 x 2.828 x 2.828) = 22.627. It would be easier for you to find the value of root 8 now with this easy method.
Here is a chart of the square roots of numbers from 1 to 100 for your reference. You can use these values for your calculations.
\[\sqrt{1}\] | 1.000 | \[\sqrt{26}\] | 5.099 | \[\sqrt{51}\] | 7.141 | \[\sqrt{76}\] | 8.718 |
\[\sqrt{2}\] | 1.414 | \[\sqrt{27}\] | 5.196 | \[\sqrt{52}\] | 7.211 | \[\sqrt{77}\] | 8.775 |
\[\sqrt{3}\] | 1.732 | \[\sqrt{28}\] | 5.292 | \[\sqrt{53}\] | 7.280 | \[\sqrt{78}\] | 8.832 |
\[\sqrt{4}\] | 2.000 | \[\sqrt{29}\] | 5.385 | \[\sqrt{54}\] | 7.348 | \[\sqrt{79}\] | 8.888 |
\[\sqrt{5}\] | 2.236 | \[\sqrt{30}\] | 5.477 | \[\sqrt{55}\] | 7.416 | \[\sqrt{80}\] | 8.944 |
\[\sqrt{6}\] | 2.449 | \[\sqrt{31}\] | 5.568 | \[\sqrt{56}\] | 7.483 | \[\sqrt{81}\] | 9.000 |
\[\sqrt{7}\] | 2.646 | \[\sqrt{32}\] | 5.657 | \[\sqrt{57}\] | 7.550 | \[\sqrt{82}\] | 9.055 |
\[\sqrt{8}\] | 2.828 | \[\sqrt{33}\] | 5.745 | \[\sqrt{58}\] | 7.616 | \[\sqrt{83}\] | 9.110 |
\[\sqrt{9}\] | 3.000 | \[\sqrt{34}\] | 5.831 | \[\sqrt{59}\] | 7.681 | \[\sqrt{84}\] | 9.165 |
\[\sqrt{10}\] | 3.162 | \[\sqrt{35}\] | 5.916 | \[\sqrt{60}\] | 7.746 | \[\sqrt{85}\] | 9.220 |
\[\sqrt{11}\] | 3.317 | \[\sqrt{36}\] | 6.000 | \[\sqrt{61}\] | 7.810 | \[\sqrt{86}\] | 9.274 |
\[\sqrt{12}\] | 3.464 | \[\sqrt{37}\] | 6.083 | \[\sqrt{62}\] | 7.874 | \[\sqrt{87}\] | 9.327 |
\[\sqrt{13}\] | 3.606 | \[\sqrt{38}\] | 6.164 | \[\sqrt{63}\] | 7.937 | \[\sqrt{88}\] | 9.381 |
\[\sqrt{14}\] | 3.742 | \[\sqrt{39}\] | 6.245 | \[\sqrt{64}\] | 8.000 | \[\sqrt{89}\] | 9.434 |
\[\sqrt{15}\] | 3.873 | \[\sqrt{40}\] | 6.325 | \[\sqrt{65}\] | 8.062 | \[\sqrt{90}\] | 9.487 |
\[\sqrt{16}\] | 4.000 | \[\sqrt{41}\] | 6.403 | \[\sqrt{66}\] | 8.124 | \[\sqrt{91}\] | 9.539 |
\[\sqrt{17}\] | 4.123 | \[\sqrt{42}\] | 6.481 | \[\sqrt{67}\] | 8.185 | \[\sqrt{92}\] | 9.592 |
\[\sqrt{18}\] | 4.243 | \[\sqrt{43}\] | 6.557 | \[\sqrt{68}\] | 8.246 | \[\sqrt{93}\] | 9.644 |
\[\sqrt{19}\] | 4.359 | \[\sqrt{44}\] | 6.633 | \[\sqrt{69}\] | 8.307 | \[\sqrt{94}\] | 9.695 |
\[\sqrt{20}\] | 4.472 | \[\sqrt{45}\] | 6.708 | \[\sqrt{70}\] | 8.367 | \[\sqrt{95}\] | 9.747 |
\[\sqrt{21}\] | 4.583 | \[\sqrt{46}\] | 6.782 | \[\sqrt{71}\] | 8.426 | \[\sqrt{96}\] | 9.798 |
\[\sqrt{22}\] | 4.690 | \[\sqrt{47}\] | 6.856 | \[\sqrt{72}\] | 8.485 | \[\sqrt{97}\] | 9.849 |
\[\sqrt{23}\] | 4.796 | \[\sqrt{48}\] | 6.928 | \[\sqrt{73}\] | 8.544 | \[\sqrt{98}\] | 9.899 |
\[\sqrt{24}\] | 4.899 | \[\sqrt{49}\] | 7.000 | \[\sqrt{74}\] | 8.602 | \[\sqrt{99}\] | 9.950 |
\[\sqrt{25}\] | 5.000 | \[\sqrt{50}\] | 7.071 | \[\sqrt{75}\] | 8.660 | \[\sqrt{100}\] | 10.000 |
1. How to Simplify the Value of Root 8?
Simplifying the value of root 8 is simple and easy to follow. If you follow these easy steps, you will be able to simplify it easily.
For simplifying the root 8 value, first, write √8 as 2^{2} x 2. This is the factorized form of the root 8 value.
Taking the whole root of the value 2^{2} x 2, you get √4 x √2.
Now, take out 4 from the radical since √4 value is 2.
After doing this you will get 2√2.
Hence, the exact value of √8 is 2√2.
2. What is the Exact Value of the Root of 8 in Decimal Form?
The exact value of root 8 can be calculated with the help of a calculator. When you manually find the value of root 8, you get 2√2. But, since √2 leads you to a decimal number, it becomes tedious to find the exact value of √2. But when you find it through the calculator, you can get the exact value of root 8.
Hence, the exact value of root 8 in the decimal form is √8 = 2.82842712475.
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