square root of 63 simplified
Understand the Problem
The question is asking for the simplified form of the square root of 63. To solve this, we will break down 63 into its prime factors and simplify the square root accordingly.
Answer
$3\sqrt{7}$
Answer for screen readers
The final answer is $3\sqrt{7}$
Steps to Solve
- Prime factorization of 63
Find the prime factors of 63. It can be written as $63 = 3^2 imes 7$.
- Simplify the square root using prime factors
Take the square root of the prime factors:
$$ \sqrt{63} = \sqrt{3^2 imes 7} $$
- Extract the perfect square factors
Extract the $3^2$ term outside of the square root:
$$ \sqrt{3^2} \times \sqrt{7} = 3 \sqrt{7} $$
The final answer is $3\sqrt{7}$
More Information
When simplifying square roots, always look for perfect square factors to extract. This often makes it easier to handle and understand.
Tips
A common mistake is to overlook the perfect square factors or to incorrectly factorize the number. Make sure to double-check the prime factors of the given number.
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