APPROXIMATING SQUARE ROOTS

Example 1 :

Approximate √40.

Solution :

40 is not a perfect square.

Find the two perfect squares surrounding 40.

They are 36 and 49.

Then, we have

36 < 40 < 49

6² < 40 < 7²

Taking square root, we have

√6² < √40 < √7²

6 < √40 < 7

From the above calculation, it is clear that the value of √40 lies between 6 and 7.

Example 2 :

Approximate √90.

Solution :

90 is not a perfect square.

Find the two perfect squares surrounding 90.

They are 81 and 100.

Then, we have

81 < 90 < 100

9² < 90 < 10²

Taking square root, we have

√9² < √90 < √10²

9 < √90 < 10

From the above calculation, it is clear that the value of √90 lies between 9 and 10.

Example 3 :

Approximate √240.

Solution :

240 is not a perfect square.

Find the two perfect squares surrounding 240.

They are 225 and 256.

Then, we have

225 < 240 < 256

15² < 240 < 16²

Taking square root, we have

√15² < √240 < √16²

15 < √240 < 16

From the above calculation, it is clear that the value of √240 lies between 15 and 16.

Example 4 :

Approximate √370.

Solution :

370 is not a perfect square.

Find the two perfect squares surrounding .

They are 361 and 400.

Then, we have

361 < 370 < 400

19² < 370 < 20²

Taking square root, we have

√19² < √370 < √20²

19 < √370 < 20

From the above calculation, it is clear that the value of √370 lies between 19 and 20.

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