Question

A calculator shows that 2 ≈ 1.414 and 3 ≈ 1.732. Use linear interpolation to estimate 2.2 . Hint: Find the number that is 0.2 of the difference between 1.414 and 1.732 and add this number to the smaller number, 1.414. Round your estimate to the nearest thousandth.

Answer 1

Answer:

Step-by-step explanation:

Given that a calculator shows that 2 ≈ 1.414 and 3 ≈ 1.732.

i.e. using calculators square root of irrational numbers are being found out.

We have $\sqrt{2} =1.414\\\sqrt{3} =1.732$

We have to find square root of 2.2

2.2 = 2+0.2

When 2 increases to 3 square root increases by 0.318

In the same rate if increase is there if 2 increases to 0.2 the increase would be

0.2*0.318 = 0.0636

Hence we can say that

$\sqrt{2.02} =1.414+0.0636\\= 1.4776$

Thus using linear interpolation we find that 2.2 has estimate for square root

as 1.4776.