csaluja wrote:

chetan2u wrote:

Karthik200 wrote:

\((1 + \sqrt{3})\sqrt{(2 + [square_root]3})[/square_root]\)

A. \(\sqrt{2}(2 - \sqrt{3})\)

B. \(\sqrt{2}(2 + \sqrt{2})\)

C. \(\sqrt{2}(2 + \sqrt{3})\)

D. \(\sqrt{2}(3 + \sqrt{3})\)

E. \(\sqrt{3}(2 + \sqrt{3})\)

Guys, sorry for the poor question formatting. I tried my best to make it proper. However, the square root inside the square root is somehow not appearing properly. Kindly, use the attachment to view the question.

Let x be the value of the equation..

\(X=(1+√3)(\sqrt{2+√3})\)...

So \(x^2=(1+3+2√3)(2+√3)=(4+2√3)(2+√3)=2(2+√3)(2+√3)=2(2+√3)^2\)..

Therefore x=√2*(2+√3)

C

Hi Chetan,

I was wondering could you please explain how you went from 2(2+√3)^2 to √2*(2+√3)? Would greatly appreciate it!

Hi

csaluja,

Here \(x^2=2*(2+√3)^2\) (I hope you are clear till this point)

Taking square root both sides, we have

\(\sqrt{x^2}=\sqrt{2*(2+√3)^2}=\sqrt{2}*\sqrt{(2+√3)^2}\)

(You know \(\sqrt{a*b}=\sqrt{a}*\sqrt{b}\))

Or, \(x=\sqrt{2}*(2+√3)\)

Hope it helps.

_________________

Regards,

PKN

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