Question

Approximate square root 18 to the nearest hundredth. Be sure to show all of your work.​

Answer 1

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:

• 16 and 25

As $\sf \sqrt{16}=4$ and $\sf \sqrt{25}=5$ then $\sf 4 < \sqrt{18} < 5$

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):

$\sf \implies \dfrac{4+4.5}{2}=4.25$

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

$\sf \implies \dfrac{4.25+\frac{72}{17}}{2}=\dfrac{577}{136}=4.242647059$

Repeat:

⇒ 18 ÷ 577/136 = 2448/577

$\sf \implies \dfrac{\frac{577}{136}+\frac{2448}{577}}{2}=4.242640687$

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)

Answer 2

Answer:

The square root of 18 with one digit decimal accuracy is 4.2.

Step-by-step explanation: