Question

estimate the value of following to nearest to one decimal place
1) √90
2)√150
3)√600

Answer 1

Answer:

1) √90 ≈ 9.5

2) √150 ≈ 12.2

3) √600 ≈ 24.5

Step-by-step explanation:

We know that

√90 ≈ 9.4868

To approximate 9.4868 to one decimal place we have to look on second digit after point.

"If it is greater then 5 then we will add 1 in first digit  after point."

In our case it is 8 which is greater then 5 so we add 1 in 4 to get 5

And

√90 ≈ 9.5

Now

√150 ≈ 12.2474

Here second digit after point is 4 which is less then 5 so we will not add 1

And so

√150 ≈ 12.2

Now

√600 ≈ 24.4948

Here second digit after point is 9 which is greater then 5.So we add 1 in 4 to get 5.

And

√600 ≈ 24.5

Answer 2

Step-by-step explanation:

To estimate the value of this number to one decimal place, the easiest way is to first find the factors and then round of the result. The prime factorization is helpful to make the calculations easier and can be done in less time.

√90

The prime factorization of 90 = 2*3*3*5

√90 = 3√10 = 3*3.162 = 9.486 = 9.5

Similarly,

√150 = 2*3*5*5

√150 = 5√2√3 = 5*1.414*1.732 = 12.247 = 12.2

Similarly,

√600 = 2*3*2*5*2*5

√600 = 10√2√3 = 29.494 = 29.5