Gujarat BoardEnglish MediumSTD 8MATHSSquares and Square Roots5 Marks
Question
Using square root table, find the square root, $\frac{101}{169}$
✓
Answer
$\sqrt{\frac{101}{169}}=\frac{\sqrt{101}}{\sqrt{169}}$ The square root of $101$ is not listed in the table.
This is because the table lists the square roots of all the numbers below $100$.
Hence, we have to manipulate the number such that we get the square root of a number less than $100$.
This can be done in the following manner, $\sqrt{101}=\sqrt{1.01\times100}=\sqrt{1.01}\times10$
Now, we have to find the square root of $1.01$ We have, $\sqrt{1}=1$ and $\sqrt{2}=1.414$
Their difference of $1\ (2 - 1)$, the difference in the values of the square roots is $0.414$ For the difference of $0.01$,
the difference in the values of the square roots is, $0.01\times0.414=0.00414$
$\therefore\sqrt{1.01}=1+0.00414=1.00414$
$\sqrt{101}=\sqrt{1.01}\times10=1.00414\times10=10.0414$
Finally, $\sqrt{\frac{101}{169}}=\frac{\sqrt{101}}{1313}=\frac{10.0414}{13}=0.772$
This value is really close to the one from the key answer.
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