Question

How do you simplify `sqrt 2(sqrt2-sqrt 3)`?

Answer 1

`2-sqrt6`

Explanation:

`sqrt2(sqrt2-sqrt3)`

Expand,

`sqrt2*sqrt2-sqrt2*sqrt3`

Simplify,

`2-sqrt6`

Answer 2

`2-sqrt(6)`

Explanation:

Did you know that if you had, say `sqrt(a)xxsqrt(b)` it is the same as `sqrt(axxb)`

Not in this question but also `sqrt(a)/sqrt(b) = sqrt(a/b)`
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Given: `color(blue)(sqrt(2))color(green)((sqrt(2)-sqrt(3))`

Multiply everything inside the bracket by the `color(blue)(sqrt(2))` that is outside it.

`color(green)( [ color(white)(2/2)color(blue)(sqrt(2))xxsqrt(2)color(white)(2/2)]-[ color(white)(2/2)color(blue)(sqrt(2))xxsqrt(3)color(white)(2/2)] )`

`color(green)(color(white)("dd")sqrt(2xx2)color(white)("ddddd")-color(white)("d")color(white)("d")sqrt(2xx3)`

`color(green)(color(white)("dddddddddddd")2-sqrt(6)`