QUESTION 1: 1.1 Given: $$ \sqrt{9+25} ; \pi-4 ; \sqrt[3]{-27} ; \frac{2}{3} ; \frac{18}{2} ; \sqrt{-27} $$ From the list given above, write down: 1.1.1 A natural number. 1.1.2 A negative irrational number. 1.1.3 A non-real number. 1.1.4 A rational number which is not an integer. 1.2 Between which two consecutive integers does $$ \sqrt{138} $$ lie?

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1.1.1 A natural number is a positive integer. From the given list, the natural number is $$ \frac{18}{2} = 9 $$.

1.1.2 A negative irrational number is a number that is negative and cannot be expressed as a finite decimal or fraction. From the given list, the negative irrational number is $$ \sqrt{-27} $$.

1.1.3 A non-real number is a number that is not a real number. From the given list, the non-real number is $$ \sqrt{-27} $$ because it involves the square root of a negative number.

1.1.4 A rational number which is not an integer is a number that can be expressed as a fraction but is not a whole number. From the given list, the rational number which is not an integer is $$ \frac{2}{3} $$.

1.2 To determine between which two consecutive integers $$ \sqrt{138} $$ lies, we need to find the square root of 138 and then round it to the nearest integer.

Let's calculate the square root of 138:
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{138}$$
The square root of 138 is approximately 11.74734.

Therefore, $$ \sqrt{138} $$ lies between the two consecutive integers 11 and 12.
1.1.1 Natural number: 9 1.1.2 Negative irrational number: √(-27) 1.1.3 Non-real number: √(-27) 1.1.4 Rational number that is not an integer: 2/3 1.2 √138 lies between 11 and 12.

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