Simplify the square root of 24.
Understand the Problem
The question is asking how to simplify the square root of 24, which involves breaking down the number into its prime factors and simplifying the square root based on those factors.
Answer
2\sqrt{6}
Answer for screen readers
The simplified square root of 24 is 2\sqrt{6}
Steps to Solve
- Prime factorization of 24
Prime factorize 24 to break it down into its prime components.
$$ 24 = 2 \times 2 \times 2 \times 3 $$
- Simplify inside the square root
Group the prime factors pairs inside the square root. Each pair can be taken out as a single number.
$$ \sqrt{24} = \sqrt{2 \times 2 \times 2 \times 3} = \sqrt{(2 \times 2) \times 6} = \sqrt{4 \times 6} $$
- Take square roots of perfect squares
Identify the perfect square (in this case, 4) and take its square root out of the radical sign.
$$ \sqrt{4 \times 6} = 2 \sqrt{6} $$
The simplified square root of 24 is 2\sqrt{6}
More Information
Simplifying square roots helps in various mathematical problems by reducing the complexity of the numbers involved.
Tips
A common mistake is not properly grouping pairs of prime factors inside the square root. Ensure that for each pair, you take out one of those numbers.
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