Question

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

Answer 1

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

Explanation:

Answer 2

4.24 (nearest hundredth)

Explanation:

Step 1

Square numbers: 1, 4, 9, 16, 25, 36, ...

Find the perfect squares either side of 18:

• 16 and 25

As
`\sf √(16)=4` and
`\sf √(25)=5` then
`\sf 4 < √(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 (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 (4.25+(72)/(17))/(2)=(577)/(136)=4.242647059`

Repeat:

⇒ 18 ÷ 577/136 = 2448/577

`\sf \implies ((577)/(136)+(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)