What is the square root of 820?
Understand the Problem
The question is asking for the square root of the number 820. To solve this, we will need to calculate the value that, when multiplied by itself, equals 820.
Answer
$28.64$
Answer for screen readers
The square root of 820 is approximately $28.64$.
Steps to Solve
- Set up the equation for the square root We want to find a number $x$ such that when multiplied by itself equals 820. This can be expressed as:
$$ x^2 = 820 $$
- Take the square root of both sides To isolate $x$, we take the square root of both sides of the equation:
$$ x = \sqrt{820} $$
- Simplify the square root We can simplify $\sqrt{820}$ by breaking it down into its prime factors. The prime factorization of 820 is $4 \times 205$ and $205$ can be further factored into $5 \times 41$. Therefore, we can rewrite:
$$ \sqrt{820} = \sqrt{4 \times 205} = \sqrt{4} \times \sqrt{205} = 2\sqrt{205} $$
- Approximate the square root To find an approximate numerical value for $\sqrt{205}$, we can use a calculator.
Calculating it gives approximately:
$$ \sqrt{205} \approx 14.32 $$
So multiplying this by 2 gives:
$$ 2\sqrt{205} \approx 2 \times 14.32 \approx 28.64 $$
The square root of 820 is approximately $28.64$.
More Information
The square root of a number represents the value that, when multiplied by itself, gives the original number. The square root of 820 can be expressed in simplified radical form as $2\sqrt{205}$, showing a deeper understanding of its factorization.
Tips
- Confusing the square root symbol with squaring a number. Remember, $\sqrt{x}$ means "what number squared equals $x$."
- Forgetting to simplify the square root, leading to answers that are not in simplest form.