square root of 175
Understand the Problem
The question is asking for the square root of the number 175, which requires calculation to arrive at the simplest radical form or a decimal approximation.
Answer
$5\sqrt{7}$ or 13.2288
Answer for screen readers
The final answer is $5\sqrt{7}$ or approximately 13.2288.
Steps to Solve
- Factorize the number inside the square root
Factorize 175 into its prime factors.
$175 = 5^2 × 7$
- Simplify the square root using the prime factors
Split the square root into the product of square roots of the prime factors.
$\sqrt{175} = \sqrt{5^2 × 7} = \sqrt{5^2} × \sqrt{7} = 5 \sqrt{7}$
- Provide the final simplified form
The simplified radical form of $\sqrt{175}$ is $5\sqrt{7}$.
Alternatively, for decimal approximation, use a calculator.
$\sqrt{175} \approx 13.2288$
The final answer is $5\sqrt{7}$ or approximately 13.2288.
More Information
Not all numbers have a simple radical form, but in this case, 175 simplifies nicely because it includes a square number (25) as a factor.
Tips
A common mistake is to miss the square factor within the number. Always try to factorize the number completely to catch any square factors.
AI-generated content may contain errors. Please verify critical information
