Question

Give an approximation of underroot(3) correct to hundredths. (Round to two decimal places as needed.)

Answer 1

Answer: 1.75

Explanation:

To find the value of
`√(3)`

`\text{Let , }y=√(x)`

`\text{And Let x = 4 and }\Delta x=-1`

Now,

`\Delta y=√(x+\Delta x)-√(x)\\\\=√(3)-√(4)=√(3)-2\\\\\Rightarrow\ √(3)=\Delta y+2`

Since dy is approximately equals to
`\Delta y` then ,

`dy=(dy)/(dx)\Delta x\\\\=(1)/(2√(x))*(-1)=(1)/(2√(4))*(-1)=-0.25`

Thus , the approximate value of
`√(3)=-0.25+2=1.75`