Question

Estimay square root of rational numbers in the form of fractions

$\sqrt \frac{29}{78}$
​

Answer 1

Step-by-step explanation:

Solution

Consider the numerator i.e. 29.

The nearest square numbers to 29 are 25 and 36.

We know that

$\bf5^ 2 =25<29<6^ 2 =36$

$\bf \Rightarrow5< \sqrt 29 <6$

Since 29 is much closer to 25 than to 36,

√29 is approximately 5.

Now consider the denominator i.e. 78.

We know that

$\bf8^ 2 =64<78<9^ 2 =81$

The nearest square numbers to 78 are 64 and 81.

$\bf \Rightarrow8< \sqrt 78 <9$

Since 78 is much closer to 81 than to 64,

√78 is approximately 9.

$\bf \: Thus, \: sqrt \frac{29}{78} is \: approximately \frac{5}{9}$