Gujarat BoardEnglish MediumSTD 8MATHSSquares and Square Roots5 Marks
Question
Using square root table, find the square root, $4955$
✓
Answer
On prime factorisation, $4955$ is equal to $5 \times 991$, which means that $\sqrt{4955}=\sqrt{5}\times\sqrt{11}$
The square root of $991$ is not listed in the table, it 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.
$\sqrt{4955}=\sqrt{49.55\times100}=\sqrt{49.55}\times10$
Now, we have to find the square root of $49.55$ We have, $\sqrt{49}=7$ and $\sqrt{50}=7.071$
Their difference is $0.071$ Thus, for the difference of $1\ (50 - 49)$, the difference in the values of the square roots is $0.071$ For the difference of $0.55$, the difference in the values of the square is, $0.55\times0.0701=0.03905$
$\therefore\sqrt{49.55}=7+0.3905=7.03905$
Finally, we have $\sqrt{4955}=\sqrt{49.55}\times10$
$=7.03905\times10=70.3905$
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