Estimate the value of the following to the nearest to one decimal place of √150
The Correct Answer and Explanation is:
The square root of 150, to one decimal place, is:
√150 ≈ 12.2
Explanation
To estimate the square root of 150, we are trying to find a number which, when multiplied by itself, gives a value close to 150. This process is useful in mathematics and science when working with measurements, geometry, and real-world applications that require approximations.
First, let’s find two perfect squares that 150 lies between:
- 144=12\sqrt{144} = 12 (since 122=14412^2 = 144)
- 169=13\sqrt{169} = 13 (since 132=16913^2 = 169)
So, 150\sqrt{150} is between 12 and 13. Now, we can narrow it down:
Try 12.212.2:
12.2×12.2=148.8412.2 \times 12.2 = 148.84
Try 12.312.3:
12.3×12.3=151.2912.3 \times 12.3 = 151.29
Since 150 is between 148.84 and 151.29, we see that 12.2 is closer to √150 than 12.3 is. Therefore, to one decimal place:
√150 ≈ 12.2
Why Estimating Square Roots Matters
In many real-life scenarios, especially when using calculators isn’t allowed or when precision is flexible, estimating square roots helps us understand the scale or size of a value. Engineers, scientists, and students often estimate square roots to quickly analyze data or check for calculation errors.
This method of approximation is also a stepping stone to more advanced topics like solving quadratic equations, understanding irrational numbers, and using number sense. In fact, the square root of 150 is an irrational number, which means it has an infinite number of non-repeating decimal places and cannot be expressed exactly as a fraction.
In conclusion, estimating √150 gives us a value of 12.2 to one decimal place, which is a practical and useful approximation in many contexts.
