Question : The value of $\sqrt{2\sqrt[3]{4\sqrt{2\sqrt[3]{4\sqrt{2\sqrt[3]{4.......}}}}}}$ is:
Option 1: 2
Option 2: $2^{2}$
Option 3: $2^{3}$
Option 4: $2^{5}$
Answer (1)
20th Jan, 2024
Correct Answer: 2
Solution :
Let $x=\sqrt{2\sqrt[3]{4\sqrt{2\sqrt[3]{4\sqrt{2\sqrt[3]{4.......}}}}}}$
By squaring both sides, we get,
$⇒x^{2} =2×\sqrt[3]{{4×x}}$
By cubing both sides, we get:
$⇒x^{6}=8×4x$
$⇒x^{5}=32=2^{5}$
$\therefore x=2$
Hence, the correct answer is 2.
Comments (0)
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Result | Eligibility | Application | Selection Process | Preparation Tips | Admit Card | Answer Key
Get Updates Brochure
Thank You!
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
Upcoming Exams
Mains Exam
Application Date:
13 Dec, 2024
- 19 Dec, 2024
Mains Exam
Admit Card Date:
6 Dec, 2024
- 14 Dec, 2024
Admit Card Date:
20 Nov, 2024
- 15 Dec, 2024
Exam Date:
15 Dec, 2024
- 15 Dec, 2024
Application Date:
9 Dec, 2024
- 30 Dec, 2024
