Question

3√6×2√3=...
5√12+3√3=...​

Answer 1

• 
  `3√(6)* \:2√(3)=18√(2)`

• 
  `5√(12)+3√(3)=13√(3)`

Explanation:

1)

Given the expression

`3√(6)\:* \:2√(3)`

`\mathrm{Factor\:integer\:}6=3* \:2`

`=3√(3* \:2)* \:2√(3)`

`\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}`

`=3√(3)√(2)* \:2√(3)`

`\mathrm{Apply\:radical\:rule}:\quad √(a)√(a)=a`

`=3* \:2* \:3√(2)`

`=18√(2)`

Thus,

`3√(6)* \:2√(3)=18√(2)`

2)

Given the expression

`5√(12)+3√(3)`

`\:=\:5√(\left(4\right)\left(3\right))+3√(3)`

`=\:5* 2√(\left(3\right))+3√(3)`

`=10√(3)+3√(3)`

`\mathrm{Add\:similar\:elements:}\:10√(3)+3√(3)=13√(3)`

`=13√(3)`

Thus,

`5√(12)+3√(3)=13√(3)`