Simplify 2/^6sqrt8
I need all of the steps.
Thanks
/ followed by ^ makes no sense.
What number is being raised to the sixth, or 6sqrt 8, power?
Is the / a typing error?
You know that sometimes before a square root sign you have a number that is raised like an exponent.
To simplify the expression 2/(6√8), we need to simplify the denominator and then divide the numerator by it.
Step 1: Simplify the denominator.
The denominator of the expression is 6√8. To simplify this, we first write 8 as a product of its factors: 8 = 2 × 2 × 2. We can then rewrite the square root of 8 as the square root of each factor multiplied together: 6√8 = 6√(2 × 2 × 2).
Step 2: Simplify the square root.
Next, we simplify the square root by taking out the perfect square factors from under the square root sign. In this case, there is a perfect square factor of 2^2 = 4. Therefore, we can rewrite the expression as: 6√(2 × 2 × 2) = 6 × 2√2 = 12√2.
Step 3: Divide the numerator by the simplified denominator.
Now that we have simplified the denominator to 12√2, we can divide the numerator, which is 2, by the denominator. This gives us the final simplified expression: 2/(6√8) = 2/12√2.
Step 4: Further simplify the fraction.
To simplify the fraction 2/12, we can divide both the numerator and denominator by their greatest common divisor, which is 2. Dividing 2 by 2 gives us 1, and dividing 12 by 2 gives us 6. So, the fraction simplifies to 1/6.
The final simplified expression is 1/6√2.