Question

I need help with finding the rational approximation of 37 using perfect squares

Answer 1

For rational approximation of 37, it means we are to obtain the close estimate for the square root of 37.

using perfect squares,

The perfect square number immediately lower than 37 is

`36`

The perfect square number immediately higher than 37 is

`49`

Then we set up the problem as in the image below

The distance between 36 to 37 is lower than the distance between 49 to 37, hence the rational aproximation of 37 will be closer to the square root of 36 than the square root of 49.

This accouunt for the sqaure root of 37 in the image above

`\sqrt[]{37}=6.08\approx6.1`

Therefore

The rational aprosimation of 37 using perfect square is 6.1