Math Problem Statement
What is the product of (3√2)(5√10)?
Solution
We are asked to find the product of .
Step-by-Step Solution:
- Multiply the whole numbers: .
- Multiply the square roots: .
Thus, the product is:
-
Simplify :
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Multiply this by 15:
So, the final answer is:
Would you like further details or have any questions?
Here are five related questions to extend your understanding:
- How do you multiply two square roots like ?
- Can all square roots be simplified? Why or why not?
- What is the result of squaring a square root, like ?
- How do you simplify expressions involving square roots and whole numbers together?
- What are some real-world applications where square roots are used?
Tip: When simplifying square roots, always look for perfect squares inside the radical (like or ) to simplify your expression further.
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Math Problem Analysis
Mathematical Concepts
Algebra
Radicals
Multiplication of Square Roots
Formulas
a√b × c√d = ac√(b × d)
√ab = √a × √b
Theorems
Properties of square roots
Multiplication of radicals
Suitable Grade Level
Grades 9-10