Math Problem Statement
Simplify the given expression: √(10x³) * √(5x²)
Solution
Let's simplify the given expression, which is:
We can first combine the square roots using the property:
So we get:
Next, simplify the square root:
Since , the expression becomes:
Thus, the simplified form is:
This matches the last answer choice.
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Related Questions:
- How do you simplify products of square roots in general?
- What are the properties of exponents and how are they used in simplifications?
- What is the general rule for taking square roots of variables with exponents?
- How do you factor square roots to simplify expressions?
- How would the process change if there were cube roots instead of square roots?
Tip:
When dealing with square roots, always try to simplify the radicand (the number inside the square root) by factoring out perfect squares.
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Math Problem Analysis
Mathematical Concepts
Simplifying square roots
Multiplication of square roots
Exponents
Formulas
√a * √b = √(a * b)
√(x^n) = x^(n/2) when n is even
Theorems
Square root property: √(a) * √(b) = √(a * b)
Suitable Grade Level
Grades 9-11