What is the square root of 3969?

Understand the Problem

The question is asking for the square root of 3969, which involves finding a number that, when multiplied by itself, results in 3969.

Answer

The square root of 3969 is $63$.

Steps to Solve

Set up the equation

To find the square root of 3969, we want to find a number $x$ such that:

$$ x^2 = 3969 $$

Estimate the square root

To solve for $x$, we can first estimate by finding the perfect squares around 3969. Noticing that $60^2 = 3600$ and $70^2 = 4900$, we can narrow it down to check numbers between 60 and 70.

Check for perfect squares

Now, we can check our estimates by squaring the integers between 60 and 70.

Calculate $62^2$:

$$ 62^2 = 3844 $$

Calculate $63^2$:

$$ 63^2 = 3969 $$

At this point, we've found that:

$$ 63^2 = 3969 $$

Conclusion

Thus, the square root of 3969 is $x = 63$.

The square root of 3969 is $63$.

More Information

Finding the square root involves determining what number, when multiplied by itself, gives the original number. The process includes estimating and checking perfect squares, as seen here.

Tips

A common mistake is to miscalculate the squares of numbers. Always double-check calculations, especially for numbers close to your estimates.

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