The general algebraic expression is used for evaluating the value of square root 5. The given value of [tex]\left[\rm G_3 \right][/tex] and the value of [tex]\left [\rm 5 \div G_3 \right][/tex] are identical. So, the approximate value of [tex]\sqrt{5}[/tex] will be 2.236.
To find the approximate value of [tex]\sqrt{5}[/tex], the below method can be used:
- In first step it is given that [tex]\rm G_1 = 2[/tex], so the value of [tex]\rm 5 \div G_1[/tex] can be evaluated from the below expression:
[tex]\rm \dfrac{5}{G_1} = \dfrac{5}{2} = 2.25[/tex]
- In second step It is given that [tex]\rm G_2 = 2.25[/tex], so the value of [tex]\rm 5\div G_2[/tex], can be evaluated from the below expression::
[tex]\rm \dfrac{5}{G_2}=\dfrac{5}{2.25}=2.23[/tex]
- Now, in third step it is given that [tex]\rm G_3 = 2.236[/tex], so the value of [tex]\rm 5\div G_3[/tex] is given by:
[tex]\rm \dfrac{5}{G_3}=\dfrac{5}{2.236} = 2.236[/tex]
Here, we can see that the given value of [tex]\rm G_3[/tex] and the of [tex]\rm 5 \div G_3[/tex] are same so, the approximate value of [tex]\sqrt{5}[/tex] is 2.236.
For more information, refer the link given below
https://brainly.com/question/2785661
