Question

Find the square root of 85 correct to the nearest tenth.

Answer 1

B. 9.2

Explanation

The square root can be approximated with the next formula:

`√(x)\approx(x+y)/(2√(y))`

where y is the nearest number to have an exact root.

In this case, we need to calculate the square root of x = 85. Using y = 81, we get:

`\begin{gathered} x\approx(85+81)/(2√(81)) \\ x\approx(166)/(2\cdot9) \\ x\approx(162+4)/(18) \\ x\approx(162)/(18)+(4)/(18) \\ x\approx9+(2)/(9) \\ x\approx9+0.222... \\ x\approx9.2 \end{gathered}`