QQuestionMathematics
QuestionMathematics
"Simplify.
Remove all perfect squares from inside the square root. √175 ="
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Answer
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Step 1:I'll solve this step-by-step, carefully following the LaTeX formatting guidelines:
Step 2:: Factor the number under the square root
175 = 5^{2} \times 7
First, let's find the prime factorization of 175
Step 3:: Identify the perfect square factor
We can see that $$5^{2}$$ is a perfect square factor inside the square root.
Step 4:: Separate the perfect square from the remaining factor
\sqrt{175} = \sqrt{5^{2} \times 7} = \sqrt{5^{2}} \times \sqrt{7}
Step 5:: Simplify the perfect square term
\sqrt{5^{2}} = 5
Step 6:: Rewrite the expression
\sqrt{175} = 5\sqrt{7}
Final Answer
Key insights: - Perfect squares inside a square root can be simplified - The goal is to remove perfect square factors from under the radical - The remaining factor stays under the square root
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