Questions and Answers
What is the simplest form of the radical expression $4 rac{1}{4} \sqrt{2x} + 6 \frac{1}{4} \sqrt{2x}$?
10 \frac{1}{4} \sqrt{2x}
If a rope is $\sqrt{250}$ units long and is cut into two pieces, what is the length of the longer piece expressed in simplest radical form?
3 \sqrt{10}
What is the simplest form of the expression $\sqrt[3]{750} + \sqrt[3]{2058} - \sqrt[3]{48}$?
10 \sqrt[3]{6}
What is the product of the radical expression $(7 - \sqrt{7})(-6 + \sqrt{7})$?
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How can you write the expression $\frac{\sqrt{3} - \sqrt{6}}{\sqrt{3} + \sqrt{6}}$ with a rationalized denominator?
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Study Notes
Radical Expressions and Simplification
- The radical expression 4⁴√2x + 6⁴√2x simplifies to 10 ⁴√2x.
- Simplification involves combining like terms that share the same radical factor.
Simplifying Lengths of Segments
- A rope with a length of √250 units can be cut into two pieces.
- The length of the longer piece, when expressed in simplest radical form, is 3 √10 units.
Combining Cube Roots
- The expression ³√750 + ³√2058 - ³√48 simplifies to 10 ³√6.
- Combining cube roots requires identifying common factors and simplifying where possible.
Calculating Products of Radical Expressions
- The product of (7 - √7) and (-6 + √7) results in the expression -49 + 13 √7.
- Distributing each term can help in effectively calculating products involving radicals.
Rationalizing Denominators
- The expression (√3 - √6) / (√3 + √6) can be rewritten with a rationalized denominator as -3 + 2 √2.
- Rationalization improves the presentation of fractions involving radicals by eliminating radical expressions from the denominator.
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Description
Test your understanding of binomial radical expressions with this set of flashcards. Each card presents a different problem requiring you to simplify radical expressions or apply radical concepts. Challenge yourself and enhance your algebra skills!
