Welcome! Today we'll learn how to calculate the square root of 8. The square root of a number is a value that, when multiplied by itself, gives the original number. We need to find what number multiplied by itself equals 8.
The first and most direct method is to use a calculator. When you input the square root of 8, you get approximately 2.828. We can verify this by multiplying 2.828 by itself, which gives us approximately 8.
The second method is to simplify the radical. First, we find the largest perfect square factor of 8, which is 4. We can write 8 as 4 times 2. Then we use the property that the square root of a product equals the product of square roots. This gives us the square root of 4 times the square root of 2, which simplifies to 2 times the square root of 2.
Now let's convert our simplified radical form to decimal. We know that the square root of 2 is approximately 1.414. So 2 times the square root of 2 equals 2 times 1.414, which gives us 2.828. This matches exactly with our calculator result from the first method!
To summarize what we've learned: The square root of 8 can be calculated using a calculator to get approximately 2.828. We can also simplify it to the radical form 2 times the square root of 2. Both methods give us the same decimal result. The simplified radical form is often preferred in mathematics because it shows the exact relationship.