Question

How would you simplify `sqrt2 times 5 sqrt2`?

Answer 1

`10`

Explanation:

Multiplying radicals is similar to regular multiplying. You will multiply the terms outside the square roots together and multiply the terms inside the square root together.

`sqrt2 xx 5sqrt2`

Let's change it a little to give the first quantity a number outside the square root:

`1sqrt2 xx 5sqrt2`

Anything multiplied by `1` is itself, so it doesn't change the value of the expression for it to be there.

Now multiply the outside numbers and inside numbers together:

`1 xx 5sqrt(2xx2)`

`5sqrt4`

`5(2) rarr 10`

Answer 2

`10`

Explanation:

Given: `sqrt2*5sqrt2`

Rearrange into:

`=>sqrt2*sqrt2*5`

`=(sqrt2)^2*5`

`=2*5`

`=10`