AP ICET 2019 Shift 1 Paper

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Question : 81 of 200

Marks: +1, -0

√{8+2√{15}}

=

$√3-√5$
$√5-√3$
$√3+√5$
$3+√5$

Solution:

Let

√{(8+2√{15})}=√x+√y

Squaring on both sides

8 + 2√15 = (x + y) + 2√xy;

x+y=8

….(1) and

4xy = 60

;

(x-y)^{2}=8^{2}-60=4;

(x-y)=2

....(2)
Solving (1) and (2) ;

x = 5

and

y = 3

;

√{(8+2√{15})}=√5+√3

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