Question

Simplify this expression.

Answer 1

Answer:
`√(10) + √(15) - √(14) -√(21)`

Explanation:

`(√(2) + √(3) ) (√(5) -√(7) )`

Apply the distributive property by multiplying each term of
`√(2) + √(3)` by each term of
`√(5) - √(7)`.

`√(2) √(5) - √(2) √(7) + √(3) √(5) - √(3) √(7)`

To multiply
`√(2)` and
`√(5)` multiply the numbers under the square root.

`√(10) - √(2)√(7) + √(3) √(5) - √(3) √(7)`

To multiply
`√(2)` and
`√(7)` multiply the numbers under the square root.

`√(10) -√(14) + √(3) √(5) -√(3) √(7)`

To multiply
`√(3)` and
`√(5)` multiply the numbers under the square root.

`√(10) - √(14) + √(15) -√(3) √(7)`

To multiply
`√(3)` and
`√(7)` multiply the numbers under the square root.

`√(10) - √(14) + √(15) - √(21)`

Hope it helps and have a great day! =D

Answer 2

`√(10) +√(15) -√(14) -√(21)`

Explanation:

Let's first distribute the √2 :

`√(2) (√(5) )-√(2)( √(7) )=√(10) -√(14)`

Now we can distribute the √3 :

`√(3) (√(5))- √(3) (√(7) )=√(15) -√(21)`

Now we add these two together to get :

`√(10) +√(15) -√(14) -√(21)`