Simplify \[\sqrt {10\dfrac{{151}}{{225}}} \].
Answer
281.4k+ views
Hint: In the given question, we have to find the square root of a mixed number \[\sqrt {10\dfrac{{151}}{{225}}} \]. In order to solve it, first we will have to convert the number into an improper fraction and then find out it’s square root easily.
A mixed number is a combination i.e. a mixture of the whole number and a fraction expressed together as a single number. It is partly a whole number and partly a fraction.
Complete step by step solution:
The fraction can be proper or improper. Proper fraction is the one where the numerator is less than the denominator whereas improper fraction is the one where numerator is more than the denominator.
Examples of mixed number are - \[12\dfrac{3}{{20}}\],\[7\dfrac{5}{{16}}\], \[8\dfrac{2}{7}\] etc.
We can convert a mixed number into improper fraction by following the below given steps:
Step One: Multiply the whole number by the denominator
Step Two: Add the answer from Step One to the numerator
Step Three: Write the answer of Step Two over the denominator.
We can solve the given sum as follows:
First converting \[10\dfrac{{151}}{{225}}\] into improper fraction-
Step One: Multiplying \[10\]with the denominator of improper fraction \[225\] i.e. \[10 \times 225\]
\[ = 2250\]
Step Two: Adding the above answer to the numerator of the improper fraction i.e. \[2250 + 151\]
\[ = 2401\]
Step Three: Forming the improper fraction with above answer as numerator i.e. \[\dfrac{{2401}}{{225}}\]
Hence, we have converted the mixed number into improper fraction, \[10\dfrac{{151}}{{225}} = \dfrac{{2401}}{{225}}\].
Now we can find the square root by prime factorization method since they are perfect squares:
\[\sqrt {\dfrac{{2401}}{{225}}} \]
=\[\sqrt {\dfrac{{49 \times 49}}{{15 \times 15}}} \]\[ = \sqrt {\dfrac{{{{(49)}^2}}}{{{{(15)}^2}}}} \]
\[ = \dfrac{{49}}{{15}}\]
Therefore, \[\sqrt {10\dfrac{{151}}{{225}}} = \dfrac{{49}}{{15}}\].
Note:
> To find the square root of any number, we need to check whether the given number is a perfect square or not.
> If it is a perfect square then we can solve it by prime factorization method.
> If it is not a perfect square, then we will need to use the division method.
A mixed number is a combination i.e. a mixture of the whole number and a fraction expressed together as a single number. It is partly a whole number and partly a fraction.
Complete step by step solution:
The fraction can be proper or improper. Proper fraction is the one where the numerator is less than the denominator whereas improper fraction is the one where numerator is more than the denominator.
Examples of mixed number are - \[12\dfrac{3}{{20}}\],\[7\dfrac{5}{{16}}\], \[8\dfrac{2}{7}\] etc.
We can convert a mixed number into improper fraction by following the below given steps:
Step One: Multiply the whole number by the denominator
Step Two: Add the answer from Step One to the numerator
Step Three: Write the answer of Step Two over the denominator.
We can solve the given sum as follows:
First converting \[10\dfrac{{151}}{{225}}\] into improper fraction-
Step One: Multiplying \[10\]with the denominator of improper fraction \[225\] i.e. \[10 \times 225\]
\[ = 2250\]
Step Two: Adding the above answer to the numerator of the improper fraction i.e. \[2250 + 151\]
\[ = 2401\]
Step Three: Forming the improper fraction with above answer as numerator i.e. \[\dfrac{{2401}}{{225}}\]
Hence, we have converted the mixed number into improper fraction, \[10\dfrac{{151}}{{225}} = \dfrac{{2401}}{{225}}\].
Now we can find the square root by prime factorization method since they are perfect squares:
\[\sqrt {\dfrac{{2401}}{{225}}} \]
=\[\sqrt {\dfrac{{49 \times 49}}{{15 \times 15}}} \]\[ = \sqrt {\dfrac{{{{(49)}^2}}}{{{{(15)}^2}}}} \]
\[ = \dfrac{{49}}{{15}}\]
Therefore, \[\sqrt {10\dfrac{{151}}{{225}}} = \dfrac{{49}}{{15}}\].
Note:
> To find the square root of any number, we need to check whether the given number is a perfect square or not.
> If it is a perfect square then we can solve it by prime factorization method.
> If it is not a perfect square, then we will need to use the division method.
Recently Updated Pages
Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts
Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is the past tense of read class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What is pollution? How many types of pollution? Define it

Give 10 examples for herbs , shrubs , climbers , creepers

Which state has the longest coastline in India A Tamil class 10 social science CBSE

Write an application to the principal requesting five class 10 english CBSE
