Question

Estimate the square root of 150 to the nearest tenth.

Answer 1

the answer is 12.2 for 150 rounded to nearest tenth

Answer 2

Square root of 150 to the nearest tenth is 12.2

Solution:

Given Data:
`√(150)` we need to find the nearest tenth of the value.

Follow the below steps to solve the problem:

Rewrite 150 as
`5^(2) * 6`

`√(150)=\sqrt{5^(2) * 6}`

`5^(2)` can be expanded as
`5 * 5`

Now the above expression becomes,

`√(150)=√(5 * 5 * 6)`

We know that
`√(5 * 5)=5` Hence the above expression becomes,

`√(150)=5 √(6)`

The result can be shown in multiple forms.

Exact Form:
`5 √(6)`

Decimal Form:
`5 √(6)=5 * 2.4494 \approx 12.247`

Now we have to round to nearest tenth. So the nearest tenth in

Round it to the nearest tenth so we get 12.247 is “2”

The number which is to right of nearest tenth is less than 5

So the numbers to right of nearest tenth disappears. So we get 12.2

Hence the square root of 150 to the nearest tenth is 12.2