Can someone please help me? simplify: 3 √(98xy) - √(108xy \:) \: + 2 √(75xy) 21 √(2xy) \: + |1| √( |2| )

Question

Can someone please help me?

simplify:

`3 √(98xy) - √(108xy \:) \: + 2 √(75xy)`

`21 √(2xy) \: + |1| √( |2| )`

Answer 1

For each square root, you can simplify the expression under the root as

`3√(98xy)=3√(2\cdot7^2xy)=3\cdot7√(2xy)=21√(2xy)`

`√(108y)=√(2^2\cdot3^3xy)=2\cdot3√(3xy)=6√(3xy)`

`2√(75xy)=2√(3\cdot5^2xy)=2\cdot5√(3xy)=10√(3xy)`

So we have

`3√(98xy)-√(108xy)+2√(75xy)=21√(2xy)-6√(3xy)+10√(3xy)`

`=21√(2xy)+4√(3xy)`

This means [1] = 4 and [2] =
`3xy`.