Find the square root of $9\dfrac{{49}}{{64}}$.

Hint- First solve the mixed fraction and turn this into improper fractions i.e. $\dfrac{p}{q}$ form. Then, we take the square root of this fraction and obtain the answer and then convert it back into a mixed fraction.

Complete step by step answer:
As given,
$9\dfrac{{49}}{{64}}$
Now, we solve the given mixed fraction by multiplying the denominator with the whole number and adding the numerator to the answer and then write it as a numerator and the value of the denominator will remain the same.
By following this method, we get an improper fraction
$ = \dfrac{{625}}{{64}}$
And then by taking its square root we get
$ = \sqrt {\dfrac{{625}}{{64}}} = \sqrt {\dfrac{{25 \times 25}}{{8 \times 8}}} $
By further solving it, we will get
$ = \dfrac{{25}}{8}$
Since, the answer is also an improper fraction we convert it again to mixed fraction
Now let’s convert the improper fraction into mixed fraction by dividing the numerator with the denominator, then write the quotient as the whole number and write the remainder as numerator and the denominator will be written as in denominator as it is in the fraction part. This will give us the mixed fraction of the improper fraction.
$ = 3\dfrac{1}{8}$

Hence, our answer is $3\dfrac{1}{8}$

Note- In this question solving mixed fractions is the main part. Now, mixed fraction consists of two parts – a whole number and a fraction part. Any improper fraction should always be converted to a mixed fraction by the method described above. Solve the mixed fractions carefully and change the improper fraction into mixed fraction step by step as many students get confused while solving this.