simplifying square roots

(1+ root 3)^2 = 1+3+ (2 root 3)
= 4 + 2 root3
= 2( 2+root 3)

=> 1 + root 3 = (root 2) ( root( 2+ root 3)) ...

Substitute this value of (1 + root3) in the above expression
we get,

(root 2) ( root(2+ root3))*( root(2- root 3)) = (root 2) (root( 4-3))
{ using (a-b)(a+b) = (a^2 - b^2) }

So answer= (root 2)

Now, can we have the OA please :roll:

IMO answer is 2

Nice thinking mohit. OA is root 2

square the whole expression - thats it.

we get (after squaring)

(1+3+2√3) (2-√3) = 2

so answer is √2

OA is 2.

a. (1+root3)=(root1+root3)=(root4)=2
b. (root(2-root3))=(root(root4-root3)=(root1)=1

So 2*1=2

GambitOS wrote:OA is 2.

a. (1+root3)=(root1+root3)=(root4)=2
b. (root(2-root3))=(root(root4-root3)=(root1)=1

So 2*1=2

one, OA is "official answer".
so when you give your answer don't say that it's the OA until you are sure that it's the OA
now,
(root1+root3)=(root4)=2--Wrong
(root1 + root3) is not equal to root(1+3)
root(root4-root3)=(root1)=1--wrong
(root4-root3) is not equal to root(4-3)

Thanks! You are right, I am mistook. Sorry.

(1+√3)^1/2 * (1+√3)^1/2 * [1 + (1-√3)]^1/2
(1+√3)^1/2 * [1+√3+1-3]^1/2
(1+√3)^1/2 * (√3-1)^1/2
(3-1)^1/2
√2

can't it be -sqrt(2) too?