Calculate √100 × √25: Multiplying Square Roots Step-by-Step

Square Root Multiplication with Perfect Squares

Solve the following exercise:

10025= \sqrt{100}\cdot\sqrt{25}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's solve this problem together.
00:11 First, we break down one hundred into ten times ten, which is ten squared.
00:17 Next, break down twenty-five into five times five, that's five squared.
00:23 Remember, the square root of a squared number cancels the square. Now, let's multiply.
00:29 And there you have it, that's our solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

10025= \sqrt{100}\cdot\sqrt{25}=

2

Step-by-step solution

We can simplify the expression without using the laws of exponents, because the expression has known square roots, so let's simplify the expression and then perform the multiplication:

10025=105=50 \sqrt{100}\cdot\sqrt{25}=\\ 10\cdot5=\\ \boxed{50} Therefore, the correct answer is answer D.

3

Final Answer

50 50

Key Points to Remember

Essential concepts to master this topic
  • Rule: Simplify each square root first when dealing with perfect squares
  • Technique: 100=10 \sqrt{100} = 10 and 25=5 \sqrt{25} = 5 , then multiply 10 × 5
  • Check: Verify 100×25=2500=50 \sqrt{100 \times 25} = \sqrt{2500} = 50

Common Mistakes

Avoid these frequent errors
  • Using the property √a × √b = √(ab) without simplifying first
    Don't jump to 100×25=2500 \sqrt{100} \times \sqrt{25} = \sqrt{2500} = requires calculating √2500! This makes the problem unnecessarily difficult. Always simplify perfect square roots first: √100 = 10 and √25 = 5, then multiply 10 × 5 = 50.

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

Should I always use the property √a × √b = √(ab)?

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Not always! When you have perfect squares like 100 and 25, it's much easier to simplify each square root first. Only use the property when the individual square roots don't simplify nicely.

How do I know if a number is a perfect square?

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A perfect square has a whole number square root. Common perfect squares include: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. If you're unsure, try finding what number times itself equals your value!

What if I get √2500 instead of 50?

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That's the same answer! 2500=50 \sqrt{2500} = 50 because 50 × 50 = 2500. However, it's much easier to recognize that √100 = 10 and √25 = 5 than to calculate √2500.

Can I multiply square roots that aren't perfect squares?

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Yes! For example, 2×8=16=4 \sqrt{2} \times \sqrt{8} = \sqrt{16} = 4 . The property √a × √b = √(ab) works for all positive numbers, but it's especially useful when the result is a perfect square.

Why is the answer 50 and not √50?

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Because we can simplify completely! 100=10 \sqrt{100} = 10 (exactly) and 25=5 \sqrt{25} = 5 (exactly), so 10 × 5 = 50. We don't need a square root symbol in our final answer.

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