when simplified is

Question:

$(-2-\sqrt{3})(-2+\sqrt{3})$ when simplified is

(a) positive and irrational
(b) positive and rational
(c) negative and irrational
(d) negative and rational

 

Solution:

$(-2-\sqrt{3})(-2+\sqrt{3})$

$=-(2+\sqrt{3}) \times[-(2-\sqrt{3})]$

$=(2+\sqrt{3})(2-\sqrt{3})$

$=2^{2}-(\sqrt{3})^{2} \quad\left[(a+b)(a-b)=a^{2}-b^{2}\right]$

$=4-3$

$=1$

Thus, the given expression when simplified is positive and rational.

Hence, the correct answer is option (b).

 

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now