4√2 + √2 with work

8√3 - 4√3 with work

2√3 x √32 with work

Step-by-step explanation:

4√2 + √2 = 5√2 we add 4 and the invisible 1 in front of √2, the common root stays same

8√3 - 4√3 = 4√3 subtract 4 from 8 the common root stays same

2√3 x √32 ➡ 2√3 x 4√3 too add the expressions we first need to make the roots common then add 4 and 2

1.

2.

3.

Step-by-step explanation:

Number 1:

We can treat  as a variable in which we are multiplying 4 by. Let's call x.

This makes our expression . Combining like terms, we get . This means that .

Number 2:

Again, we can use the same logic as we did in number 1. Let's treat as a variable y.

Subtracting a y term from a y term will equal the difference between the coefficients times y. So it's . This means that  

Number 3:

When we multiply radicals, we want to put the radicals in form.

is already in this form.

However is not.

is the same thing as .

Now we multiply these radicals by multiply the term inside the square root sign

384 is divisible by 64, so:

Hope this helped!