How do you simplify #(sqrt2+sqrt7)(sqrt 2+sqrt 7)#?

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Answer 1 · 2017-05-04T22:03:15

See a solution process below:

This is a special form of the quadratic factored:

#(a + b)^2 = (a + b)(a + b) = a^2 + 2ab + b^2#

Substituting #sqrt(2)# for #a# and #sqrt(7)# for #b# gives:

#(sqrt(2) + sqrt(7))(sqrt(2) + sqrt(7)) = sqrt(2)^2 + 2sqrt(2)sqrt(7) + sqrt(7)^2 =#

#2 + 2sqrt(2)sqrt(7) + 7#

We can now use this rule for multiplying radicals to simplify the middle term:

#sqrt(a) * sqrt(b) = sqrt(a * b)#

#2 + 2sqrt(2 * 7) + 7 = #2 + 2sqrt(14) + 7 =#

#9 + 2sqrt(14)#