What is the square root of 84?
Understand the Problem
The question is asking for the value of the square root of 84. This requires performing a mathematical operation to find a number that, when multiplied by itself, equals 84.
Answer
9.17
Answer for screen readers
The approximate value of the square root of 84 is 9.17
Steps to Solve
- Identify if 84 is a perfect square
Check if there is a number which, when squared, equals 84. Since 84 is not a perfect square, we need to find its approximate square root.
- Use prime factorization to find an approximate value
Factorize 84 into its prime factors to help check if there are any perfect squares that can simplify the square root.
$$84 = 2^2 imes 3 imes 7$$
- Simplify the square root using the factors
Separate the perfect square part from the non-perfect square part:
$$ \sqrt{84} = \sqrt{2^2 \times 3 \times 7} = \sqrt{2^2} \times \sqrt{3} \times \sqrt{7} = 2\sqrt{21} $$
- Approximate the value if required
If you need a numerical approximation rather than a simplified radical form, use a calculator:
$$\sqrt{84} \approx 9.17$$
The approximate value of the square root of 84 is 9.17
More Information
The square root of a number is a value that, when multiplied by itself, gives the original number. Since 84 is not a perfect square, its square root is an irrational number.
Tips
A common mistake is not simplifying the square root properly. Remember to always look for factors that are perfect squares and extract them.