Question

Order each set of cards from least to greatest. a. .,⎯⎯⎯⎯√,0.25 , comma , square root of 1 ninth end root , comma , 6 twenty fifths b. ⎯⎯⎯⎯⎯⎯⎯√,.,⎯⎯√square root of 121 over 25 end root , comma , 2.25 , comma square root of 5

Answer 1

Given:

a.
`√(0.25),\sqrt{(1)/(9)},(6)/(25)`

b.
`\sqrt{(121)/(25)},2.25,√(5)`

To find:

The correct order for each set of cards from least to greatest.

Solution:

a.
`√(0.25),\sqrt{(1)/(9)},(6)/(25)`

Convert all numbers in decimal form.

`√(0.25)=0.5`

`\sqrt{(1)/(9)}=(1)/(3)=0.333...`

`(6)/(25)=0.24`

It is clear that,

`0.24<0.33...<0.5`

`(6)/(25)<\sqrt{(1)/(9)}<√(0.25)`

Therefore, the required order is
`(6)/(25),\sqrt{(1)/(9)},√(0.25)`.

b.
`\sqrt{(121)/(25)},2.25,√(5)`

Convert all numbers in decimal form.

`\sqrt{(121)/(25)}=(11)/(5)=2.2`

`2.25` already in decimal form.

`√(5)\approx 2.236`

It is clear that,

`2.2<2.236<2.25`

`\sqrt{(121)/(25)}<√(5)<2.25`

Therefore, the required order is
`\sqrt{(121)/(25)},√(5),2.25`.