Answer:
Step-by-step explanation:
According to given equation
A = [tex]\sqrt{16} +(-\frac{21}{5})[/tex] ; [tex]\sqrt{16}[/tex] can be simplified to 4.
Sum : [tex]\sqrt{16} +(-\frac{21}{5})[/tex] =[tex]\frac{20-21}{5} =-\frac{1}{5}[/tex]
4 is a rational number and [tex](-\frac{21}{5})[/tex] is also a rational number.
Sum of two rational number is always a rational number.
Therefore, [tex]\sqrt{16} +(-\frac{21}{5})[/tex] is a rational number.
B = π+24 ; π is an irrational and 24 is a rational number.
Sum of an irrational and a rational is always a rational number.
Therefore, π+24 is an irrational number.
Sum = π+24
C = [tex]\sqrt{4} +5[/tex] ; [tex]\sqrt{4}[/tex] can be simplified to 2.
2 is a rational number and 5 is also a rational number.
Sum = 2+5=7
Sum of two rational number is always a rational number.
Therefore, [tex]\sqrt{4} +5[/tex] is a rational number.
D = [tex]\sqrt{8}[/tex]+π ; π is an irrational and [tex]\sqrt{8}[/tex] is also an irrational number.
Sum = [tex]2\sqrt{2}[/tex]+π
Sum of two irrational number is always an irrational number.
Therefore, [tex]\sqrt{8}[/tex]+π is an irrational number.
E=[tex]\sqrt{36} +\sqrt[3]{27}[/tex]; [tex]\sqrt{36}[/tex] can be simplified to 6 and [tex]\sqrt[3]{27}[/tex] can be simplified to 3.
6 is a rational number and 3 is also a rational number.
Sum = 6+3=9.
Sum of two rational number is always a rational number.
Therefore, [tex]\sqrt{36} +\sqrt[3]{27}[/tex] is a rational number.
F = [tex]\frac{3}{4} +\sqrt{27}[/tex] ; \frac{3}{4} is a rational number and \sqrt{27} an irrational number.
Sum = [tex]\frac{3}{4} +3\sqrt{3}=\frac{3+12\sqrt{3}}{4}[/tex]
Sum of an irrational and a rational is always a rational number.
Therefore, [tex]\frac{3}{4} +\sqrt{27}[/tex] is an irrational number.
