Question
Using square root table, find the square root,
4955
4955
✓
Answer
On prime factorisation,
4955 is equal to 5 × 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
$\sqrt{4955}=\sqrt{49.55}\times10$
$=7.03905\times10=70.3905$
4955 is equal to 5 × 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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