Question

4√2 + √2 with work

8√3 - 4√3 with work

2√3 x √32 with work

Answer 1

1.
`5√(2)`

2.
`4√(3)`

3.
`8√(6)`

Explanation:

Number 1:

We can treat
`√(2)` as a variable in which we are multiplying 4 by. Let's call
`√(2)` x.

This makes our expression
`4x + x`. Combining like terms, we get
`5x`. This means that
`4√(2) + √(2) = 5√(2)`.

Number 2:

Again, we can use the same logic as we did in number 1. Let's treat
`√(3)` as a variable y.

`8y-4y`

Subtracting a y term from a y term will equal the difference between the coefficients times y. So it's
`4y`. This means that
`8√(3)-4√(3)=4√(3)`

Number 3:

When we multiply radicals, we want to put the radicals in
`√(x)` form.

`√(32)` is already in this form.

However
`2√(3)` is not.

`2√(3)` is the same thing as
`√(3\cdot2^2) = √(3\cdot4) = √(12)`.

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

`√(32)\cdot√(12)=√(32\cdot12) =√(384)`

384 is divisible by 64, so:

`√(384) = √(64\cdot6) = 8√(6)`

Hope this helped!

Answer 2

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