Between which two consecutive integers does the square root lie?
1.√120
2.√56
3.√19
4.√240
5.√80
6.√27
7.√199
8.√38
9.√102
10.√11
It would also be very appreciated if you could tell me how you got it since I'm soo confused in square roots, tysm!!<3
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Answer:
im not sure if this is the answer that your looking for so
Im not going to answer all of the given square roots,but i hope this answer can help you
The value of the square root of 120 is 10.954451150103. Let us learn how to find out its value. As discussed, when a number is multiplied by itself, it gives a value whose square root can be taken. Like if write the square of a number equal to another b, we get,
b = a2
Now if we have to take the square root of b, we get,
√b = √a2
So, the root cancels the square or un-square it. Therefore we get,
√b = a
Similarly, we can find the square root of 120 here, by writing its prime factors first.
We can write, 120 = 2 × 2 × 2 × 3 × 5
Taking out the root means, taking out the pair of numbers present underneath the radix.
Therefore, the square root of 120, √120 = √(2 × 2 × 2 × 3 × 5)
⇒ √120 = 2 √(2 × 3 × 5) = 2√30
⇒ √120 = 2√30.
This is the radical form of √120. But to find the accurate value, we have to mention the value of √30. The value of the square of 30 is 5.477. Therefore,
√120 = 2 × 5.477 = 10.9544 or 2√30