The columns in the table below represent the following sets of numbers:
Natural numbers (N), Integers (Z), Rational numbers (Q),
Irrational numbers (R\Q) and Real numbers (R) - Junior Cycle Mathematics - Question (a) - 2013
Question (a)
The columns in the table below represent the following sets of numbers:
Natural numbers (N), Integers (Z), Rational numbers (Q),
Irrational numbers (R\Q) and Real nu... show full transcript
Worked Solution & Example Answer:The columns in the table below represent the following sets of numbers:
Natural numbers (N), Integers (Z), Rational numbers (Q),
Irrational numbers (R\Q) and Real numbers (R) - Junior Cycle Mathematics - Question (a) - 2013
Step 1
Complete the table by writing either 'Yes' or 'No'
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Answer
Number/Set
N
Z
Q
R\Q
R
( \sqrt{5} )
No
No
No
Yes
Yes
8
Yes
Yes
Yes
Yes
Yes
-4
No
Yes
Yes
Yes
Yes
( \frac{3}{2} )
No
No
Yes
No
Yes
3\sqrt{3}
No
No
No
Yes
Yes
4
Yes
Yes
Yes
Yes
Yes
Step 2
In the case of \( \sqrt{5} \) explain your choice in relation to the set of Irrational numbers (R\Q)
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Answer
( \sqrt{5} ) cannot be written as a fraction, indicating that it is indeed an irrational number.
Step 3
Use the properties of surds to show that \( \sqrt{8} - \sqrt{18} + \sqrt{2} \) simplifies to \( \sqrt{2} \)
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Answer
Starting from ( \sqrt{8} - \sqrt{18} + \sqrt{2} ):
