Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

If x = \( \Large \sqrt{3} + \sqrt{2} \), then the value of \( \Large \left(x + \frac{1}{x}\right) \) is

A) 2
B) 3
C) \( \Large 2\sqrt{2} \)
D) \( \Large 2\sqrt{3} \)

Correct Answer:




D) \( \Large 2\sqrt{3} \)

Description for Correct answer:

Given, \( \Large x = \sqrt{3} + \sqrt{2} \)

Therefore, \( \Large \frac{1}{x} = \frac{1}{ \left(\sqrt{3}+\sqrt{2}\right) } \times \frac{ \left(\sqrt{3} - \sqrt{2}\right) }{ \left(\sqrt{3} - \sqrt{2}\right) } \) [rationalizing]

\( \Large = \frac{1}{x} = \frac{\sqrt{3} - \sqrt{2}}{3 - 2} \)

Therefore, \( \Large x+\frac{1}{x} = \sqrt{3} + \sqrt{2} + \sqrt{3} - \sqrt{2} = 2\sqrt{3} \)

Part of solved Simplification questions and answers : >> Elementary Mathematics >> Simplification

Comments

Similar Questions

1). Find the value of \( \Large a^{3} + b^{3} + c^{3} - 3abc \) when a = 225, b = 226, c = 227

A). 2304

B). 2430

C). 2034

D). 2340

2). The value of \( \Large \frac{ \left(0.96\right)^{3} - \left(0.1\right)^{3} }{ \left(0.96\right)^{2} + \left(0.096\right) + 1 } \) is

A). 0.86

B). 1.06

C). 0.95

D). 0.97

3). Value of \( \Large \frac{\sqrt{0.0001} \times \sqrt[3]{1000000}}{\sqrt[3]{0.125} \times \sqrt[3]{0.008}} \)

A). 1

B). 10

C). 0.1

D). 0.01

4). Value of \( \Large \Large 3.5 \times (60 \div 2.5) \)

A). 1

B). 10

C). 0.1

D). 84

5). \( \Large 3\frac{2}{3} + 2\frac{3}{4} + 1\frac{1}{2} = ? \)

A). \( \Large 8\frac{11}{12} \)

B). \( \Large 10\frac{12}{13} \)

C). \( \Large 7\frac{11}{12} \)

D). \( \Large 9\frac{11}{13} \)

6). \( \Large \frac{5}{8} \times 2\frac{3}{5} \div \frac{4}{9} \)

A). \( \Large 2\frac{13}{27} \)

B). \( \Large 1\frac{11}{27} \)

C). \( \Large 2\frac{23}{32} \)

D). \( \Large 3\frac{21}{32} \)

7). \( \Large 10.8 \times 5.5 \times 8.4 = ? \)

A). 458.69

B). 489.96

C). 498.96

D). 485.69

8). \( \Large \left(4 \times 4 \times 4 \times 4 \times 4 \times 4\right)^{5} \times \left(4 \times 4 \times 4\right)^{8} \div \left(4\right)^{3} = \left(64\right)^{?} \)

A). 17

B). 10

C). 16

D). 11

9). \( \Large 8648 - 7652 = ? \times 40 \)

A). 24.7

B). 28.9

C). 27.4

D). 24.9

10). \( \Large 683.46 - 227.39 - 341.85 = ? \)

A). 114.22

B). 141.22

C). 144.22

D). 112.22