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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? $\sqrt{40}+2\sqrt{10}+\sqrt{90}$
- 4\sqrt{3}
- 5\sqrt{5}
- y\sqrt{y}
- 7\sqrt{10} (correct)
Which choice is equivalent to the expression below? $\sqrt{18}-\sqrt{2}$
Which choice is equivalent to the expression below? $\sqrt{18}-\sqrt{2}$
- 2\sqrt{2} (correct)
- 5\sqrt{2}
- 4\sqrt{2}
- 3\sqrt{2}
Which choice is equivalent to the expression below? $2\sqrt{5}+8\sqrt{5}$
Which choice is equivalent to the expression below? $2\sqrt{5}+8\sqrt{5}$
- 10\sqrt{5} (correct)
- 2\sqrt{10}
- 12\sqrt{5}
- 5\sqrt{5}
Which choice is equivalent to the expression below? $12\sqrt{-\sqrt{27}}+\sqrt{75}$
Which choice is equivalent to the expression below? $12\sqrt{-\sqrt{27}}+\sqrt{75}$
Which choice is equivalent to the expression below when $y ≠0$? $\sqrt{y^3}+\sqrt{4y^3}-2y\sqrt{y}$
Which choice is equivalent to the expression below when $y ≠0$? $\sqrt{y^3}+\sqrt{4y^3}-2y\sqrt{y}$
Which choice is equivalent to the expression below? $5x\sqrt{2}-2\sqrt{2}+2x\sqrt{2}$
Which choice is equivalent to the expression below? $5x\sqrt{2}-2\sqrt{2}+2x\sqrt{2}$
Two radical expressions are called like terms if they have the same degree and the same _____?
Two radical expressions are called like terms if they have the same degree and the same _____?
Which choice is equivalent to the expression below? $\sqrt{20}+\sqrt{45}$
Which choice is equivalent to the expression below? $\sqrt{20}+\sqrt{45}$
Which choice is equivalent to the expression below? $4\sqrt{7}-3x\sqrt{7}-x\sqrt{7}$
Which choice is equivalent to the expression below? $4\sqrt{7}-3x\sqrt{7}-x\sqrt{7}$
Which choice is equivalent to the expression below when $x ≠0$? $\sqrt{50x^3}-\sqrt{25x^3}+5\sqrt{x^3}-\sqrt{2x^3}$
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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