Simplify square root 48.
Understand the Problem
The question is asking to simplify the square root of 48. This means we need to factor 48 into its prime components and identify perfect squares to reduce the square root expression to its simplest form.
Answer
$4\sqrt{3}$
Answer for screen readers
The final answer is $4\sqrt{3}$
Steps to Solve
- Factorize the number inside the square root
First, we need to factorize 48 into its prime factors.
$$ 48 = 2 \times 24 = 2 \times 2 \times 12 = 2 \times 2 \times 2 \times 6 = 2 \times 2 \times 2 \times 2 \times 3 $$
- Identify perfect square factors
Next, we identify the perfect square factors within the prime factorization of 48. In this case, $$ 2 \times 2 \times 2 \times 2 = 16 $$, which is a perfect square ($(4^2)$), and we're left with 3.
$$ 48 = 16 \times 3 $$
- Apply the square root to the perfect square factor
Take the square root of the perfect square (16) and leave the remaining factor (3) inside the square root.
$$ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3} $$
The final answer is $4\sqrt{3}$
More Information
Simplifying square roots is a fundamental skill in algebra and it helps in different mathematical problems, including solving quadratic equations and working with geometric shapes.
Tips
A common mistake is forgetting to include the non-perfect square inside the square root after factoring. Always ensure you've correctly identified and split the perfect squares from the non-perfect squares.