simplify-the-expression-6-2-8-3-10-7-3-in-the-form-a-b-

Question Number 85864 by john santu last updated on 26/Mar/20

s i m p l i f y t h e e x p r e s s i o n

\sqrt{6 + 2 \sqrt{8 \sqrt{3} - 10}} - \sqrt{7 - \sqrt{3}} i n

t h e f o r m \sqrt{\sqrt{a} + b} ?

Answered by jagoll last updated on 26/Mar/20

by trick!

8 \sqrt{3} - 10 = 7 \sqrt{3} + \sqrt{3} - 7 - 3

= 7 (\sqrt{3} - 1) - \sqrt{3} (\sqrt{3} - 1)

= (7 - \sqrt{3}) (\sqrt{3} - 1)

let \sqrt{7 - \sqrt{3}} = x and \sqrt{\sqrt{3} - 1} = y

x^{2} + y^{2} = 7 - \sqrt{3} + \sqrt{3} - 1 = 6

hence a = 3 & b = - 1

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