Questions and Answers
Which choice is equivalent to the expression below? $\sqrt{40}+2\sqrt{10}+\sqrt{90}$
Which choice is equivalent to the expression below? $\sqrt{18}-\sqrt{2}$
Which choice is equivalent to the expression below? $2\sqrt{5}+8\sqrt{5}$
Which choice is equivalent to the expression below? $12\sqrt{-\sqrt{27}}+\sqrt{75}$
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Which choice is equivalent to the expression below when $y ≠ 0$? $\sqrt{y^3}+\sqrt{4y^3}-2y\sqrt{y}$
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Which choice is equivalent to the expression below? $5x\sqrt{2}-2\sqrt{2}+2x\sqrt{2}$
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Two radical expressions are called like terms if they have the same degree and the same _____?
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Which choice is equivalent to the expression below? $\sqrt{20}+\sqrt{45}$
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Which choice is equivalent to the expression below? $4\sqrt{7}-3x\sqrt{7}-x\sqrt{7}$
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Which choice is equivalent to the expression below when $x ≠ 0$? $\sqrt{50x^3}-\sqrt{25x^3}+5\sqrt{x^3}-\sqrt{2x^3}$
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Study Notes
Radical Expressions Simplification
- Expression Simplification: √40 + 2√10 + √90 simplifies to 7√10.
- Difference of Radicals: √18 - √2 simplifies to 2√2.
- Combining Like Terms: 2√5 + 8√5 combines to 10√5.
Identifying Equivalent Expressions
- Expression With Negative Square Root: 12√ - √27 + √75 simplifies to 4√3.
- Substituting Variables: When y ≠ 0, √(y^3) + √(4y^3) - 2y√(y) simplifies to y√y.
- Combining Radicals with Variables: 5x√2 - 2√2 + 2x√2 results in 7x√2 - 2√2.
Like Terms in Radical Expressions
- Definition of Like Terms: Two radical expressions are like terms if they share the same degree and the same radicand.
Additional Simplifications
- Sum of Radicals: √20 + √45 simplifies to 5√5.
- Combining with Variables: 4√7 - 3x√7 - x√7 simplifies to 4√7 - 4x√7.
- Complex Variable Expression: For x ≠ 0, √50x^3 - √25x^3 + 5√x^3 - √2x^3 simplifies to 4x√(2x).
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Description
Test your knowledge on simplifying radical expressions in mathematics. This quiz covers various topics, including the sum and difference of radicals, combining like terms, and identifying equivalent expressions. Perfect for mastering the concepts of radical simplification!
