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 |
Video Lessons on Square Roots
Visualising square roots
Finding Square roots
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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