Answer
468.6k+ views
Hint: Convert the numerical quantities inside square roots into perfect squares.
We have to find the square root of \[\dfrac{44100}{441}\].
Square root of \[a=\sqrt{a}={{a}^{\dfrac{1}{2}}}\]
Therefore, square root of \[\dfrac{44100}{441}=A\]
\[A=\sqrt{\dfrac{44100}{441}}={{\left( \dfrac{44100}{441} \right)}^{\dfrac{1}{2}}}\]
We can write \[44100\]as \[441\times 100\].
Hence, we get \[A={{\left( \dfrac{441\times 100}{441} \right)}^{\dfrac{1}{2}}}\]
By cancelling similar terms from numerator and denominator,
We get, \[A={{\left( 100 \right)}^{\dfrac{1}{2}}}\]
As,\[{{a}^{m}}=b\]
Then, \[a={{b}^{\dfrac{1}{m}}}\]
Similarly, \[{{\left( 10 \right)}^{2}}=100\]
\[\left( 10 \right)={{\left( 100 \right)}^{\dfrac{1}{2}}}\]
Therefore, we get \[A=10\]
Hence, the value of square root of \[\dfrac{44100}{441}\]is \[10\].
Note: Here, we also know that \[{{\left( 21 \right)}^{2}}=441\], therefore we can write \[44100\]as \[{{\left( 210 \right)}^{2}}\]and \[441\]as \[{{\left( 21 \right)}^{2}}\]and get \[A=\dfrac{210}{21}=10\]which is the correct result.
We have to find the square root of \[\dfrac{44100}{441}\].
Square root of \[a=\sqrt{a}={{a}^{\dfrac{1}{2}}}\]
Therefore, square root of \[\dfrac{44100}{441}=A\]
\[A=\sqrt{\dfrac{44100}{441}}={{\left( \dfrac{44100}{441} \right)}^{\dfrac{1}{2}}}\]
We can write \[44100\]as \[441\times 100\].
Hence, we get \[A={{\left( \dfrac{441\times 100}{441} \right)}^{\dfrac{1}{2}}}\]
By cancelling similar terms from numerator and denominator,
We get, \[A={{\left( 100 \right)}^{\dfrac{1}{2}}}\]
As,\[{{a}^{m}}=b\]
Then, \[a={{b}^{\dfrac{1}{m}}}\]
Similarly, \[{{\left( 10 \right)}^{2}}=100\]
\[\left( 10 \right)={{\left( 100 \right)}^{\dfrac{1}{2}}}\]
Therefore, we get \[A=10\]
Hence, the value of square root of \[\dfrac{44100}{441}\]is \[10\].
Note: Here, we also know that \[{{\left( 21 \right)}^{2}}=441\], therefore we can write \[44100\]as \[{{\left( 210 \right)}^{2}}\]and \[441\]as \[{{\left( 21 \right)}^{2}}\]and get \[A=\dfrac{210}{21}=10\]which is the correct result.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)