Given:
a. [tex]\sqrt{0.25},\sqrt{\dfrac{1}{9}},\dfrac{6}{25}[/tex]
b. [tex]\sqrt{\dfrac{121}{25}},2.25,\sqrt{5}[/tex]
To find:
The correct order for each set of cards from least to greatest.
Solution:
a. [tex]\sqrt{0.25},\sqrt{\dfrac{1}{9}},\dfrac{6}{25}[/tex]
Convert all numbers in decimal form.
[tex]\sqrt{0.25}=0.5[/tex]
[tex]\sqrt{\dfrac{1}{9}}=\dfrac{1}{3}=0.333...[/tex]
[tex]\dfrac{6}{25}=0.24[/tex]
It is clear that,
[tex]0.24<0.33...<0.5[/tex]
[tex]\dfrac{6}{25}<\sqrt{\dfrac{1}{9}}<\sqrt{0.25}[/tex]
Therefore, the required order is [tex]\dfrac{6}{25},\sqrt{\dfrac{1}{9}},\sqrt{0.25}[/tex].
b. [tex]\sqrt{\dfrac{121}{25}},2.25,\sqrt{5}[/tex]
Convert all numbers in decimal form.
[tex]\sqrt{\dfrac{121}{25}}=\dfrac{11}{5}=2.2[/tex]
[tex]2.25[/tex] already in decimal form.
[tex]\sqrt{5}\approx 2.236[/tex]
It is clear that,
[tex]2.2<2.236<2.25[/tex]
[tex]\sqrt{\dfrac{121}{25}}<\sqrt{5}<2.25[/tex]
Therefore, the required order is [tex]\sqrt{\dfrac{121}{25}},\sqrt{5},2.25[/tex].
