What is the square root of 69?

Understand the Problem

The question is asking for the square root of 69, which is a mathematical operation where we need to find a number that when multiplied by itself equals 69.

Answer

The square root of 69 is approximately $8.3066$.
Answer for screen readers

The square root of 69 is approximately $8.3066$.

Steps to Solve

  1. Identify the square root operation

We want to find a number $x$ such that $x^2 = 69$.

  1. Estimate the square root

To estimate $\sqrt{69}$, consider perfect squares around 69. We know that $8^2 = 64$ and $9^2 = 81$. Thus, we can conclude that:

$$ 8 < \sqrt{69} < 9 $$

  1. Use a calculator for precision

Now, using a calculator, we can compute a more precise value for $\sqrt{69}$.

The calculator gives:

$$ \sqrt{69} \approx 8.3066 $$

  1. State the approximate answer

Thus, we can conclude that the approximate value of the square root of 69 is 8.3066.

The square root of 69 is approximately $8.3066$.

More Information

The square root of a number can often be found using simple estimation techniques followed by a calculator for more precision. Estimations help in understanding the range of possible values.

Tips

  • Assuming that the square root is always a whole number can lead to incorrect conclusions, especially for non-perfect squares like 69. Always check the surrounding perfect squares.

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