Solve Square Root: Simplifying √(225/25) Step by Step

Square Root Simplification with Fraction Reduction

Solve the following exercise:

22525= \sqrt{\frac{225}{25}}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:09 Let's solve the following problem.
00:12 Calculate two hundred twenty-five divided by twenty-five.
00:17 We can break down nine as three squared.
00:20 Remember, the square root of any squared number is the number itself.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

22525= \sqrt{\frac{225}{25}}=

2

Step-by-step solution

Let's simplify the expression. First, we'll reduce the fraction under the square root, then we'll calculate the result of the root:

22525=93 \sqrt{\frac{225}{25}}= \\ \sqrt{9}\\ \boxed{3} Therefore, the correct answer is option B.

3

Final Answer

3

Key Points to Remember

Essential concepts to master this topic
  • Rule: Simplify fractions inside square roots before taking the root
  • Technique: Divide 225 ÷ 25 = 9, then find 9=3 \sqrt{9} = 3
  • Check: Verify that 3² = 9 and 9 × 25 = 225 ✓

Common Mistakes

Avoid these frequent errors
  • Taking square root of numerator and denominator separately
    Don't calculate 22525=155=3 \frac{\sqrt{225}}{\sqrt{25}} = \frac{15}{5} = 3 ! While this gives the right answer here, it's inefficient and can lead to errors with more complex fractions. Always simplify the fraction first, then take the square root.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

\( \sqrt{\frac{2}{4}}= \)

FAQ

Everything you need to know about this question

Why do I simplify the fraction first instead of taking square roots separately?

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Simplifying first makes the calculation much easier! Instead of working with larger numbers like 225 and 25, you get the simpler 9 \sqrt{9} , which is clearly 3.

What if the fraction doesn't simplify to a perfect square?

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That's fine! Simplify as much as possible first, then take the square root. For example, 502=25=5 \sqrt{\frac{50}{2}} = \sqrt{25} = 5 , but 483=16=4 \sqrt{\frac{48}{3}} = \sqrt{16} = 4 .

How do I know if 225 ÷ 25 equals 9?

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Think: "25 times what equals 225?" Since 25 × 9 = 225, we know 225 ÷ 25 = 9. You can also use long division if needed!

Can I use a calculator for this?

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You can, but try to do it by hand first! Recognizing that 225 = 15² and 25 = 5² helps you see patterns and builds your number sense.

What if I get confused about which method to use?

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Always start by simplifying the fraction under the square root. This single step will make most problems much clearer and easier to solve!

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