What is the square root of 546?

Understand the Problem

The question is asking for the square root of the number 546, which means we need to find a number that when multiplied by itself gives 546.

Answer

The square root of 546 is approximately $23.37$.

Steps to Solve

Set Up the Problem

We are looking for a number $x$ such that $x^2 = 546$. This means we need to find the square root of 546.

Use the Square Root Function

To find $x$, we take the square root of both sides of the equation:

$$ x = \sqrt{546} $$

Calculate the Square Root

Now we can either calculate this using a calculator or estimate it.

Using a calculator, we find:

$$ x \approx 23.366642 $$

Round to a Desired Decimal

Depending on the requirements, we can round this to a specific number of decimal points. For example, rounding to two decimal places gives us:

$$ x \approx 23.37 $$

The square root of 546 is approximately $23.37$.

More Information

The square root function is fundamental in mathematics and has applications in various fields, including physics and engineering. The number 23.37 is not an integer, so 546 is not a perfect square.

Tips

Not using a calculator: Many might try to guess the square root rather than calculating it accurately. Always use a calculator for precision.
Misestimating the square root: People might mistakenly think the square root is closer to the nearest perfect square, like 25 (which is $5^2$).

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