The square root of 8 in radical form is represented as √8 which is also equal to 2√2 and as a fraction, it is equal to 2.828 approximately. Squares root of a number is the number, which, on multiplying by itself gives the original number. Since 8 is not a perfect square, hence the value is represented in root form.
The value 2√2 is said to be surd, as it cannot be further simplified. As we all know, 8 = 2 × 2 × 2, thus we can see the number is a perfect cube of 2. So, we can determine the cube root of 8 which is equal to 2, such as 3√8 = 2. But for numbers which are perfect squares such as 4, 9, 16, 25, etc. the root for them can be determined easily, such as;
- √4 = √(2 x 2) = 2
- √9 = √(3 x 3) = 3
- √16 = √(4 x 4) = 4
- √25 = √(5 x 5) = 5
| Square Root of 8
√8 = 2.82842712475 Or √8 = 2.828 up to three places of decimal |
Now that you know the value of root 8, let us calculate its value here. Although finding the square root of a number by using calculators is very easy, but students should know how to calculate it manually.
The square root is represented by the symbol, ‘√’. This symbol ‘√’ is called a radical symbol or radix. The number underneath the radical symbol or radix is called as radicand.
Method to Find Value of Root 8
To give you an idea, the square of 2 is 4 and the square of 3 is 9. So, the square root of 8 essentially lies between these two digits. But, since 3 square is 9, which is greater than 8, it most probably lies between 2.8 or 2.9. The actual answer for the square root of 8 is 2.82842712475. And this is really close to our estimate. Similarly, you could use this technique to find out square roots of other numbers.
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.
Now, it’s easy to find the square root of 8, and we also learned what square root of 8 to the power of 3 is.
Also learn to find the square root of 6, 7, 9, 10, 11 and 12, by reaching to the below-mentioned links.
Square root Table From 1 to 15
In the table given here, find the values of root of numbers from 1 to 15 to use it for mathematical calculations.
| Number | Squares | Square Root (Upto 3 places of decimal) |
| 1 | 12 = 1 | √1 = 1 |
| 2 | 22 = 4 | √2 = 1.414 |
| 3 | 32 = 9 | √3 = 1.732 |
| 4 | 42 = 16 | √4 = 2.000 |
| 5 | 52 = 25 | √5 = 2.236 |
| 6 | 62 = 36 | √6 = 2.449 |
| 7 | 72 = 49 | √7 = 2.646 |
| 8 | 82 = 64 | √8 = 2.828 |
| 9 | 92 = 81 | √9 = 3.000 |
| 10 | 102 = 100 | √10 = 3.162` |
| 11 | 112 = 121 | √11 = 3.317 |
| 12 | 122 = 144 | √12 = 3.464 |
| 13 | 132 = 169 | √13 = 3.606 |
| 14 | 142 = 196 | √14 = 3.742 |
| 15 | 152 = 225 | √15 = 3.873 |
Learn more and find out unique tips and tricks to help you understand more about square roots and know how to find the square root of a number easily.
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