Question

150 estimate the square root

Answer 1

Sqrt(150) = sqrt(2×3×5×5) = 5×sqrt(6), ~ 12.25

The square root of 150 is approximately 12.25. This makes sense for the following reasons. The square root of 144 =12 and the square root of 169 =13. As 150 is between 144 and 169, it is reasonable to say that the square root of 150 must be between 12 and 13. Since 150 is closer to 144 than it is to 169, you can safely assume that the answer is probably closer to 12 than 13. So you can take a guess from here and say 12.2 or 12.3.

Or, why don’t we break this down a bit? As mentioned before, sqrt(150) = sqrt(2×3×5×5) = 5 × sqrt(6). So like before, you can estimate the square root of 6 as between 2 (or sqrt 4) and 3, (or sqrt 9). 6 is slightly closer to to 4 than it is to 9, so I would say it is probably 2.4 or 2.45. So 5 × 2.45 is 12.25.

Now, to check behind our work, we want to see what 12.25^2 is.

12.25^2 = 12.25 × 12.25 = 150.0625. That’s really close to 150, isn’t it?

Answer 2

Answer:

Approximate 12

Step-by-step explanation:

150 lies between 144 and 169

144<150<169

so, the approximate value of

$\sqrt{150} = 12$