simplify sqrt(24)
Understand the Problem
The question is asking to simplify the square root of 24, which involves finding the prime factors of 24 and simplifying the radical expression.
Answer
$2\sqrt{6}$
Answer for screen readers
The simplified form of $\sqrt{24}$ is $2\sqrt{6}$.
Steps to Solve
- Find the prime factorization of 24
To simplify the square root of 24, we first need to find the prime factors. The prime factorization of 24 is:
$$ 24 = 2^3 \times 3^1 $$
- Rewrite the square root using prime factors
Next, we can rewrite the square root of 24 using its prime factors:
$$ \sqrt{24} = \sqrt{2^3 \times 3^1} $$
- Split the radical for simplification
We can split the square root into two parts: one part for the even powers (which can be simplified) and another part for the odd powers:
$$ \sqrt{24} = \sqrt{2^2 \times 2^1 \times 3^1} = \sqrt{2^2} \times \sqrt{2^1 \times 3^1} $$
- Simplify the square root of even powers
Since $\sqrt{2^2} = 2$, we can substitute that into our equation:
$$ \sqrt{24} = 2 \times \sqrt{2 \times 3} $$
- Combine the square root terms
Now, we can combine the terms inside the square root:
$$ \sqrt{24} = 2 \times \sqrt{6} $$
The simplified form of $\sqrt{24}$ is $2\sqrt{6}$.
More Information
The square root of a number is often simplified by factoring it into its prime components. This process highlights that even powers of primes can be simplified while odd powers are left under the radical.
Tips
- Not fully factoring the number into primes can lead to errors in simplification. To avoid this, ensure all prime factors are identified correctly.
- Forgetting to simplify the even powers can result in an incorrect answer. Always check if the square root can be simplified further.
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