SQUARE ROOT of 8/3 + SQUARE ROOT of 2/3

Please see the information that Writeacher posted for you.

http://www.jiskha.com/display.cgi?id=1191442163

Is there something about her answer that you don't understand?

I would check to see if the problem is maybe the square root of 8/3 * the square root of 2/3. Maybe I am wrong, but I would look at the problem again to be sure it is definitely a sum and not a product. There is a benefit to it being a product.

To calculate the square root of a fraction, you need to find the square root of both the numerator and the denominator separately. Let's break down the calculation:

1. Square root of 8/3:
- Calculate the square root of the numerator: √8 = 2√2
- Calculate the square root of the denominator: √3
- So, the square root of 8/3 = 2√2/√3

2. Square root of 2/3:
- Calculate the square root of the numerator: √2
- Calculate the square root of the denominator: √3
- So, the square root of 2/3 = √2/√3

Now, adding both results together:

2√2/√3 + √2/√3

To add these two fractions, the denominators must be the same. Since they have a common denominator (√3), we can combine them:

(2√2 + √2)/√3

Now, simplify by combining like terms in the numerator:

3√2/√3

To rationalize the denominator (removing the square root from the denominator), multiply the numerator and denominator by √3:

(3√2)(√3)/(√3)(√3)

Simplify:

(3√6)/3

Now, cancel out the common factor of 3:

√6

Thus, the square root of 8/3 + the square root of 2/3 is √6.