227+31243\dfrac{2\sqrt{27} + 3\sqrt{12}}{4\sqrt{3}}43227+312 is equal to :
232\sqrt{3}23
323\sqrt{2}32
3
3+2\sqrt{3} + \sqrt{2}3+2
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Solving,
⇒227+31243⇒2×33+3×2343⇒63+6343⇒12343⇒3.\Rightarrow \dfrac{2\sqrt{27} + 3\sqrt{12}}{4\sqrt{3}} \\[1em] \Rightarrow \dfrac{2 \times 3\sqrt{3} + 3 \times 2\sqrt{3}}{4\sqrt{3}} \\[1em] \Rightarrow \dfrac{6\sqrt{3} + 6\sqrt{3}}{4\sqrt{3}} \\[1em] \Rightarrow \dfrac{12\sqrt{3}}{4\sqrt{3}} \\[1em] \Rightarrow 3.⇒43227+312⇒432×33+3×23⇒4363+63⇒43123⇒3.
Hence, Option 3 is the correct option.
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If x = 5−2,x+1x\sqrt{5} - 2, x + \dfrac{1}{x}5−2,x+x1 is equal to :
252\sqrt{5}25
4
454\sqrt{5}45
-4
If x = 1 + 2, then (x+1x)2\sqrt{2}, \text{ then } \Big(x + \dfrac{1}{x}\Big)^22, then (x+x1)2 is :
222\sqrt{2}22
8
424\sqrt{2}42
(5−3)2(\sqrt{5} - \sqrt{3})^2(5−3)2 is :
8+2158 + 2\sqrt{15}8+215
8+158 + \sqrt{15}8+15
8−158 - \sqrt{15}8−15
8−2158 - 2\sqrt{15}8−215
34+7\dfrac{3}{4 + \sqrt{7}}4+73 is equal to :
13(4−7)\dfrac{1}{3}(4 - \sqrt{7})31(4−7)
3(4−7)3(4 - \sqrt{7})3(4−7)
13(4+7)\dfrac{1}{3}(4 + \sqrt{7})31(4+7)
3(4+7)3(4 + \sqrt{7})3(4+7)
