Question

Simplify the following

Answer 1

`-20√(3)-5√(2)`

Explanation:

Given expression:

`4 √(12)-√(50)-7√(48)`

Rewrite 12 as 4 · 3 and 50 as 25 · 2 and 48 as 16 · 3 :

`=4 √(4 \cdot 3)-√(25 \cdot 2)-7√(16 \cdot 3)`

`\textsf{Apply radical rule} \quad √(a \cdot b)=√(a)√(b) :`

`=4 √(4)√(3)-√(25)√(2)-7√(16)√(3)`

As
`√(4)=2` and
`√(25)=5` and
`√(16)=4` then:

`=4 \cdot 2 √(3)-5√(2)-7 \cdot 4√(3)`

Simplify:

`=8√(3)-5√(2)-28√(3)`

Collect like terms:

`=8√(3)-28√(3)-5√(2)`

Combine like terms:

`=-20√(3)-5√(2)`