Podcast
Questions and Answers
What is the simplest form of the radical expression $4 rac{1}{4} \sqrt{2x} + 6 \frac{1}{4} \sqrt{2x}$?
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?
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 $\sqrt[3]{750} + \sqrt[3]{2058} - \sqrt[3]{48}$?
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 $(7 - \sqrt{7})(-6 + \sqrt{7})$?
What is the product of the radical expression $(7 - \sqrt{7})(-6 + \sqrt{7})$?
Signup and view all the answers
How can you write the expression $\frac{\sqrt{3} - \sqrt{6}}{\sqrt{3} + \sqrt{6}}$ with a rationalized denominator?
How can you write the expression $\frac{\sqrt{3} - \sqrt{6}}{\sqrt{3} + \sqrt{6}}$ with a rationalized denominator?
Signup and view all the answers
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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!
