Question

find five rational numbers between √5/7 and 4/5​

Answer 1

Could you verify that the two values are √5/7 and 4/9. I don't think it makes sense any other way.

 

√5/7 < x < 4/9

 

square everything

 

5/49 < x2 < 16/81

 

get a common denominator for the endvalues so we can compare them

 

405/3969 < x2 < 784/3969

Answer 2

Answer:

∴ Five rational numbers between √5/7 and 4/5​ are  $\frac{13}{35}, \frac{2}{5}, \frac{3}{7}, \frac{16}{35}, \frac{17}{35}$

Step-by-step explanation:

Given numbers are

$\frac{\sqrt{5} }{7} , \frac{4}{5}$

To find,

Five rational numbers between the given two numbers

Solution

We have the numbers $\frac{\sqrt{5} }{7} , \frac{4}{5}$

First, we need to find the equivalent fractions of the given fractions.

Equivalent fractions are obtained by making the denominators the same.

The denominators of the given numbers are 7 and 5

Since 5 and 7 are prime numbers =  LCM(5,7) = 5×7 = 35

To make denominators same in both the fractions we get

$\frac{\sqrt{5} }{7}= \frac{\sqrt{5} }{7} X\frac{5 }{5} = \frac{5\sqrt{5} }{35}$

$\frac{4}{5}$ = $\frac{4}{5}X\frac{7}{7}$ = $\frac{28}{35}$

The equivalent fractions of  $\frac{\sqrt{5} }{7} , \frac{4}{5}$ are $\frac{5\sqrt{5} }{35} \ and \ \frac{28}{35}$

Since$\sqrt{5}$  is approximately equal to 2.236,  $5\sqrt{5}$ is approximately equal to 11,

The rational numbers between$\frac{5\sqrt{5} }{35}$  and $\frac{28}{35}$ will also lie between $\frac{12}{35}$ and    and $\frac{28}{35}$

Hence Five rational numbers between  $\frac{12}{35}$ and    and $\frac{28}{35}$

= $\frac{13}{35}, \frac{14}{35}, \frac{15}{35}, \frac{16}{35}, \frac{17}{35}$

= $\frac{13}{35}, \frac{2}{5}, \frac{3}{7}, \frac{16}{35}, \frac{17}{35}$

∴ Five rational numbers between √5/7 and 4/5​ are $\frac{13}{35}, \frac{2}{5}, \frac{3}{7}, \frac{16}{35}, \frac{17}{35}$

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