Square root of 116 simplified
Understand the Problem
The question is asking for the simplification of the square root of 116. To solve it, we will find the prime factorization of 116 and then simplify the square root by extracting perfect squares.
Answer
\( 2 \sqrt{29} \)
Answer for screen readers
The simplified form of the square root of 116 is ( 2 \sqrt{29} ).
Steps to Solve
- Find the Prime Factorization of 116
Start by dividing 116 by the smallest prime number, which is 2.
$$ 116 \div 2 = 58 $$
Now, divide 58 by 2 again to continue finding factors.
$$ 58 \div 2 = 29 $$
Next, we check if 29 is a prime number; it only has two factors, 1 and 29. Therefore, the prime factorization of 116 is:
$$ 116 = 2^2 \times 29 $$
- Simplify the Square Root
Now, we can simplify the square root of 116 using the prime factorization:
$$ \sqrt{116} = \sqrt{2^2 \times 29} $$
We can extract $2^2$ out of the square root:
$$ \sqrt{116} = \sqrt{2^2} \times \sqrt{29} = 2 \sqrt{29} $$
The simplified form of the square root of 116 is ( 2 \sqrt{29} ).
More Information
The expression ( 2 \sqrt{29} ) represents the simplest form of the square root of 116, where ( \sqrt{29} ) cannot be simplified further since 29 is a prime number.
Tips
- Forgetting to fully factor a number when looking for prime factors.
- Not simplifying the square root correctly by neglecting to factor out perfect squares.
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