Question

rationalize root six divided by root three minus root two.
`(√(6) )/(√(3)-√(2) )`

Answer 1

`\huge\boxed{(\sqrt6)/(\sqrt3-\sqrt2)=3\sqrt2+2\sqrt3}`

Explanation:

`(\sqrt6)/(\sqrt3-\sqrt2)\\\\\text{use}\ (a-b)(a+b)=a^2-b^2\\\\(\sqrt6)/(\sqrt3-\sqrt2)\cdot(\sqrt3+\sqrt2)/(\sqrt3+\sqrt2)=(\sqrt6(\sqrt3+\sqrt2))/((\sqrt3-\sqrt2)(\sqrt3+\sqrt2))=((\sqrt6)(\sqrt3)+(\sqrt6)(\sqrt2))/((\sqrt3)^2-(\sqrt2)^2)`

`\text{use}\ √(a)\cdot√(b)=√(ab)\ \text{and}\ (√(a))^2=a`

`=(√((6)(3))+√((6)(2)))/(3-2)=(√(18)+√(12))/(1)=√(9\cdot2)+√(4\cdot3)\\\\=\sqrt9\cdot\sqrt2+\sqrt4\cdot\sqrt3=3\sqrt2+2\sqrt3`

Answer 2

the answer is

`3 √(2) + 2 √(3)`

Explanation:

the explanation is given in the image.