square root of 32 in simplest radical form
Understand the Problem
The question is asking for the square root of 32 expressed in its simplest radical form. To solve this, we will factor 32 into its prime factors and simplify the radical accordingly.
Answer
$4\sqrt{2}$
Answer for screen readers
The simplest radical form of the square root of 32 is $4\sqrt{2}$.
Steps to Solve
- Factor 32 into prime factors
To find the square root of 32, we first need to break down 32 into its prime factors.
$$ 32 = 2^5 $$
- Express the square root as a product of square roots
Next, we can express the square root of 32 using its prime factorization:
$$ \sqrt{32} = \sqrt{2^5} $$
To simplify, we can separate the powers of 2:
$$ \sqrt{32} = \sqrt{2^4 \cdot 2^1} $$
- Simplify the square root
Now, we take the square root of the perfect square, $2^4$:
$$ \sqrt{32} = \sqrt{2^4} \cdot \sqrt{2^1} $$
$$ \sqrt{32} = 2^2 \cdot \sqrt{2} $$
- Combine to get the final answer
Combine the simplified terms together:
$$ \sqrt{32} = 4\sqrt{2} $$
The simplest radical form of the square root of 32 is $4\sqrt{2}$.
More Information
The square root of 32 can be expressed in simpler terms, which is useful in various mathematical contexts, such as geometry, engineering, and physics. Understanding how to simplify radicals allows for easier calculations and clearer expressions.
Tips
- Confusing the simplification of $ \sqrt{32} $ leading to errors in identifying the perfect squares.
- Forgetting to separate the factors correctly when breaking down the square root into prime numbers.
