Question

How do you simplify `3sqrt50*sqrt22`?

Answer 1

`30sqrt11`

Explanation:

`3sqrt50*sqrt22`

`3sqrt(25*2)*sqrt22 rarr 25` is a perfect square and can be taken out of the radical

`3*5sqrt2*sqrt22`

`15sqrt2*sqrt22`

`15sqrt(2*22)`

`15sqrt44`

`15sqrt(4*11) rarr 4` is a perfect square

`15*2sqrt11`

`30sqrt11`

Answer 2

I'm going to try to write out your question mathematically:
`root(3)(50xxsqrt22)`

Explanation:

To solve this exceedingly complicated question, let's start by converting everything into indices.

But first, we should simplify your equation:
`root(3)(sqrt55000)`
Now the question will be written in indicial form as:
`(55000^(1/2))^(1/3)`

By the power law of indices `->` `(a^m)^n=a^(mn)`, this would make the indices `1/2xx1/3=1/6`.
Therefore, the question will now become:
`55000^(1/6)`
`=root(6)55000`
`=50root(6)22`
In surd form.

I hope this helps!

Answer 3

`30sqrt11`

Explanation:

`3sqrt50*sqrt 22`

`:.=3 sqrt(2*5*5)*sqrt(2*11)`

`:.=sqrt 5*sqrt 5=5`

`:.=3*5 sqrt 2*sqrt 2*sqrt 11`

`:.=15 sqrt 2*sqrt 2*sqrt 11`

`:.=sqrt2*sqrt2=2`

`:.=2*15*sqrt 11`

`:.=30 sqrt11`