Answer:
4.24 (nearest hundredth)
Step-by-step explanation:
Step 1
Square numbers: 1, 4, 9, 16, 25, 36, ...
Find the perfect squares either side of 18:
As [tex]\sf \sqrt{16}=4[/tex] and [tex]\sf \sqrt{25}=5[/tex] then [tex]\sf 4 < \sqrt{18} < 5[/tex]
Step 2
Divide 18 by one of the two square roots in step 1 (4 or 5):
⇒ 18 ÷ 4 = 4.5
Step 3
Find the average of the root (4) and the result (4.5):
[tex]\sf \implies \dfrac{4+4.5}{2}=4.25[/tex]
Repeat steps 2 and 3:
Divide 18 by the solution of step 3. Then find the average of this and the solution of step 3:
⇒ 18 ÷ 4.25 = 72/17
[tex]\sf \implies \dfrac{4.25+\frac{72}{17}}{2}=\dfrac{577}{136}=4.242647059[/tex]
Repeat:
⇒ 18 ÷ 577/136 = 2448/577
[tex]\sf \implies \dfrac{\frac{577}{136}+\frac{2448}{577}}{2}=4.242640687[/tex]
As the approximate square root needs to be to the nearest hundredth, we do not need to keep repeating the steps.
Therefore, √18 ≈ 4.24 (nearest hundredth)
