What is the square root of 189?
Understand the Problem
The question is asking for the square root of the number 189, which is a mathematical operation. To solve this, we will apply the process of finding the square root either by estimation or using a calculator.
Answer
The approximate value of $\sqrt{189}$ is $13.747$.
Answer for screen readers
The square root of 189 is approximately $13.747$.
Steps to Solve
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Estimation Strategy To estimate the square root of 189, we can look for two perfect squares between which 189 lies. The closest perfect squares are $144$ ($12^2$) and $196$ ($14^2$). Hence, we know that: $$ 12 < \sqrt{189} < 14 $$
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Using a Calculator for Precision Next, let's use a calculator to find a more precise value of $\sqrt{189}$.
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Final Calculation Using a calculator, we find that: $$ \sqrt{189} \approx 13.747 $$
The square root of 189 is approximately $13.747$.
More Information
The number 189 is not a perfect square, which is why we need to approximate its square root. Knowing the perfect squares helps in estimating its value.
Tips
- Rounding too early: Ensure that the final approximation is done after calculating the square root, not during.
- Forgetting to check perfect squares: Always identify surrounding perfect squares to help with estimation.
