Question

approximate each irrational number to the nearest hundredth without using a calculator square root of 118 and 319​

Answer 1

`√(118)\approx 10.86`

`√(319)\approx 17.86`

Explanation:

Consider the provided number.

We need to find the approximate value of
`√(118)` to the nearest hundredth.

First find two perfect squares that the irrational number falls between.

`100<118<121`

118 is lying between 100 and 121, therefore the square root value of 118 will be somewhere between 10 and 11.

`√(100)<√(118)<√(121)`

`10<√(118)<11`

118 is closer to 121 as compare to 100.

Therefore,
`√(118)\approx 10.86`

Consider the number
`√(319)`

First find two perfect squares that the irrational number falls between.

`289<319<324`

319 is lying between 289 and 324, therefore the square root value of 319 will be somewhere between 17 and 18.

`√(289)<√(319)<√(324)`

`17<√(319)<18`

319 is closer to 324 as compare to 289.

Therefore,
`√(319)\approx 17.86`