Question

Find the square root of $11\dfrac{9}{{81}}$.

Answer 1

Hint: In the above question we will convert the mixed fraction into improper fraction. Then, we will find the square root of the given fraction.

Complete step-by-step answer:
Convert the mixed fraction into improper fraction - $11\dfrac{9}{{81}} = \dfrac{{900}}{{81}}$
Now, Square root of $\dfrac{{900}}{{81}}$= $\sqrt {\dfrac{{900}}{{81}}} = \sqrt {\dfrac{{{{30}^2}}}{{{9^2}}}} = \dfrac{{30}}{9} = \dfrac{{10}}{3}$

Additional Information: A mixed number is a combination of a whole number and a proper fraction represented together. It represents a number between any two whole numbers. A mixed number is formed by combining three parts – a whole number, a numerator, and a denominator. The numerator and denominator are the part of the proper fraction that forms the mixed fraction. Mixed fraction is partly a whole number and partly a fraction. We can convert mixed fraction into improper fraction in the following ways – first multiply the denominator with the whole number. Then add the numerator of the fraction to the result. Keep the denominator the same. Then the improper fraction will be obtained.
Proper fraction – When the numerator is less than the denominator.
Improper fraction – When the numerator is greater than denominator.
Mixed fraction – It is an improper function, which is written as a combination of a whole number and a fraction.
The square root of any number is equal to a number, which when squared gives the original number. Example - $\sqrt {a.a} = \sqrt {{a^2}} = a$

Note: To find the square root of any number, we need to see whether the given number is a perfect square or imperfect square. If the number is a perfect square, such as 4, 9, 16, 25, 49 etc., then we can factorize the number by prime factorization method. If the number is an imperfect square, such as 2, 3, 5, 7 etc., then we have to use a long division method to find the root.