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SSC CGL Exam  >  SSC CGL Questions  >  The expression[(√2)√2]√2giv... Start Learning for Free
The expression [(√2)√2]√2 gives
  • a)
    a natural number
  • b)
    a integer and not a natural number
  • c)
    a rational number but not an integer.
  • d)
    a real number but not a rational number
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The expression[(√2)√2]√2givesa)a natural numberb)a i...
Given expression = [(√2)√2]√2
= (√2)(2)√2/2
= (√2)(2)1/√2
= (2)1/2 x 21/√2
= 2(2/21/√2)
= (2)(2)(1/√2 - 1)
which denotes a real number but not a rational number .
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Most Upvoted Answer
The expression[(√2)√2]√2givesa)a natural numberb)a i...

Explanation:

Given Expression:
- The expression is [(√2)√2]√2

Solution:
- Simplifying the expression step by step:
1. (√2)√2 = √(2*2) = √4 = 2
2. Now, [2]√2 = 2√2

- Therefore, the given expression simplifies to 2√2.

Classification:
- The expression 2√2 is a real number but not a rational number because it cannot be expressed as a ratio of two integers.
- The number √2 is irrational, and multiplying it by 2 does not change its irrationality.
- Hence, the final result is a real number but not a rational number.

Therefore, option 'D' - a real number but not a rational number is the correct classification for the given expression.
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The expression[(√2)√2]√2givesa)a natural numberb)a integer and not a natural numberc)a rational number but not an integer.d)a real number but not a rational numberCorrect answer is option 'D'. Can you explain this answer?
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