How do you multiply a whole number by a radical, and how do you add a whole number and a radical

How do you multiply a whole number by a radical? Also, how do you ADD a whole number with a radical? Thanks!

You just write the number next to the radical when multiplying. For example...

5*√x = 5√x
You could always stick the number inside if you wanted to like this
√25x

Because a number and a radical aren't like terms the simplest form of the expression 5 + √x is the expression itself, 5 + √x. However, if you had something like 5√x + √x, the simplified form would be 6√x (think of it as there being a 1 outside the 2nd radical).

for example,

2 times √3

is the same as

2(√1) times 1√3

multiply the outisde by outside, inside by inside

2(1) times √(1x3)

2 √3





If you're more confused about:

5 x 3√2

multiply the outside by the outside:

15√2




3 + √48

you can only simplify the radical.

3 + (√16 x 3)

3 + (4 x √3)

3 + 4√3

can't simplify further.