Answer

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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.

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