Question

Simplify sqrt72 -3sqrt12 + sqrt 192

Answer 1

`6√(2)+2{\sqrt3}`

Explanation:

Given expression:

`√(72)-3√(12)+√(192)`

Rewrite 72 as (36 · 2), 12 as (4 · 3), and 192 as (64 · 3):

`\implies √(36 \cdot 2)-3√(4 \cdot 3)+√(64 \cdot 3)`

Apply the radical rule
`√(a \cdot b)=√(a)√(b)` :

`\implies √(36)√(2)-3√(4)√(3)+√(64){\sqrt3}`

Rewrite 36 as 6², 4 as 2², and 64 as 8²:

`\implies √(6^2)√(2)-3√(2^2)√(3)+√(8^2){\sqrt3}`

Apply the radical rule
`√(a^2)=a` :

`\implies 6√(2)-3\cdot 2√(3)+8{\sqrt3}`

Simplify:

`\implies 6√(2)-6√(3)+8{\sqrt3}`

`\implies 6√(2)+2{\sqrt3}`

Answer 2

6√2+2√3

Explanation:

We want to simplify the following radical expression

`\displaystyle √(72) - 3 √(12) + √(192)`

Recall that

`√(ab) = √(a) √(b) , \forall \text{a and b such that a$\geq$0,b$\geq$0}`

Utilizing the formula yields,

`√(72) \implies √(36 \cdot 2) \implies 6 √(2)`

`√(12) \implies √(4\cdot 3) \implies 2 √(3)`

`√(192) \implies √(64\cdot 3) \implies 8 √(3)`

So,

`6 √(2)-3\cdot2 √(3)+8 √(3)`

Carry out multiplication:

`\implies 6 √(2)-6 √(3)+8 √(3)`

Add the like terms:

`\boxed{6 √(2)+2 √(3)}`

and we're done!