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. $\sqrt{0.25},\sqrt{\dfrac{1}{9}},\dfrac{6}{25}$

b. $\sqrt{\dfrac{121}{25}},2.25,\sqrt{5}$

To find:

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

Solution:

a. $\sqrt{0.25},\sqrt{\dfrac{1}{9}},\dfrac{6}{25}$

Convert all numbers in decimal form.

$\sqrt{0.25}=0.5$

$\sqrt{\dfrac{1}{9}}=\dfrac{1}{3}=0.333...$

$\dfrac{6}{25}=0.24$

It is clear that,

$0.24$

$\dfrac{6}{25}$

Therefore, the required order is $\dfrac{6}{25},\sqrt{\dfrac{1}{9}},\sqrt{0.25}$.

b. $\sqrt{\dfrac{121}{25}},2.25,\sqrt{5}$

Convert all numbers in decimal form.

$\sqrt{\dfrac{121}{25}}=\dfrac{11}{5}=2.2$

$2.25$ already in decimal form.

$\sqrt{5}\approx 2.236$

It is clear that,

$2.2$

$\sqrt{\dfrac{121}{25}}$

Therefore, the required order is $\sqrt{\dfrac{121}{25}},\sqrt{5},2.25$.