Question

# Find the square root of $\dfrac{44100}{441}$.

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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.