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

2 Answers
Evan
Mar 25, 2018

2-sqrt6

Explanation:

sqrt2(sqrt2-sqrt3)

Expand,

sqrt2*sqrt2-sqrt2*sqrt3

Simplify,

2-sqrt6

Tony B
Mar 25, 2018

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)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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)

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