A) Sum of \[2+\sqrt{3}\]and its inverse
B) Square root of 18
C) Square root of \[7+4\sqrt{3}\]
D) None of the above
Correct Answer: A
Solution :
| Sol. [a] a. Inverse of \[2+\sqrt{3}\] |
| \[=\frac{1}{2+\sqrt{3}}\times \frac{2-\sqrt{3}}{2-\sqrt{3}}=2-\sqrt{3}\] |
| \[\therefore \] Sum \[=2+\sqrt{3}+2-\sqrt{3}=4,\] Rational number. |
| b. Square root of \[18=\sqrt{18}=3\sqrt{2},\]. Irrational number. |
| c. Square root of \[7+4\sqrt{3}=\sqrt{7+4\sqrt{3}}\] |
| \[=\sqrt{4+3+4\sqrt{3}}=\sqrt{{{2}^{2}}+{{(\sqrt{3})}^{2}}+2\cdot 2\cdot \sqrt{3}}\] |
| \[=\sqrt{{{(2+\sqrt{3})}^{2}}}=2+\sqrt{3}\] Irrational number. |
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