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

2 Answers
Mar 25, 2018

Answer:

#2-sqrt6#

Explanation:

#sqrt2(sqrt2-sqrt3)#

Expand,

#sqrt2*sqrt2-sqrt2*sqrt3#

Simplify,

#2-sqrt6#

Mar 25, 2018

Answer:

#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)#