Question

How do you simplify `sqrt8*sqrt10`?

Answer 1

Arrange the equation and get `4sqrt5`

Explanation:

`sqrt8timessqrt10 = sqrt(80)` under one square root. Further,

`=sqrt(16times5) = 4sqrt(5)`

This is the shortest form. Your answer is `4sqrt5`

Answer 2

`sqrt8sqrt10=color(blue)(4sqrt5`

Explanation:

Simplify:

`sqrt8sqrt10`

Prime factorize `8`.

`sqrt((2xx2)xx2)*sqrt10`

`2sqrt2*sqrt10`

`2sqrt(2xx10)`

`2sqrt(20)`

Prime factorize `20`.

`2sqrt((2xx2)xx5)`

Simplify.

`2xx2sqrt5`

Simplify.

`4sqrt5`

Answer 3

`4sqrt(5)`

Explanation:

short answer:
you know that when multiplying roots they can go 'in each other' thus:
`sqrt(8)* sqrt (10)` = `sqrt(8*10)`

then break down each number to it's primary numbers

`sqrt((2*2*2)*(2*5))`

notice that we have numbers that are repeated twice (because here we have a square root)
`sqrt((2*2)*(2*2)*5)`

then take them out of the square root. I took them out one at a time.
`2sqrt((2*2)*5)`
Note that when you take them out you put only one repeated term

take the second 2 out and remember this is all multiplication so 2 is multiplied by the 2 in front of the square root.

`(2*2)sqrt(5)`

the `sqrt(5)` cannot be simplified, so we leave it as it is. (there is not a whole numbers that we can multiply by itself to get 5 )

so we are left with just simplifying the front `2*2 = 4` thus

`4sqrt(5)`

Note: this could be also solved as:
`sqrt((2*2)*(2*2)*5) = sqrt(4*4*5)`
thus 4 will be our repeated twice number, then we simply would take it out to get :
`4sqrt(5)`

The second way would be more useful when dealing with larger numbers.

I hope this helps. thank you.