# 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

1. 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.

1. 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.

$$84 = 2^2 imes 3 imes 7$$

1. Simplify the square root using the factors

Separate the perfect square part from the non-perfect square part:

$$\sqrt{84} = \sqrt{2^2 \times 3 \times 7} = \sqrt{2^2} \times \sqrt{3} \times \sqrt{7} = 2\sqrt{21}$$

1. 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.

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