Question

Look at these numbers:

12.77 ,-36 ,√27 √500 , 61/12, -3√8
Write irrational numbers/
a)√27
​b) √500
c) -3√8
d) All of the above

Answer 1

The numbers √27, √500, and -3√8 are all irrational numbers because they involve the square roots of numbers that are not perfect squares, which results in non-terminating and non-repeating decimal representations. Hence, the correct answer is d) All of the above.

Step-by-step explanation:

The student has asked to identify which of the given numbers are irrational numbers. An irrational number is a number that cannot be expressed as a simple fraction, meaning its decimal representation is non-terminating and non-repeating. Looking at the numbers given: √27, √500, and -3√8, we can determine if each is irrational:

• √27 = 3√3. Since the square root of 3 is an irrational number, √27 is also an irrational number.
• √500 = 10√5. Since the square root of 5 is an irrational number, √500 is also an irrational number.
• -3√8 = -3√(2×2×2) = -6√2. Since the square root of 2 is an irrational number, -3√8 is also an irrational number.

All the above numbers are irrational. Therefore, the correct answer to the student's question is d) All of the above.