Podcast Beta
Questions and Answers
What is the simplified form of √75𝑎𝑎 + 8√3 − 9√3𝑎𝑎?
What does √𝟕𝟕𝟕 mean when simplified?
What is the result of √25?
Which rule allows you to combine surds like 5√3 and 8√3?
Signup and view all the answers
In the expression √75𝑎𝑎 + 8√3 − 9√3𝑎𝑎, what does the term √75 represent?
Signup and view all the answers
What happens when you divide 16𝒂^2 𝒃^3 by 8𝒂 𝒃?
Signup and view all the answers
After simplifying 5𝑐𝑐^8 / 4𝑐𝑐^2, what is the result?
Signup and view all the answers
What is the result of dividing 9𝑎^3 𝑏^3 by 9𝑎^4 𝑏^3?
Signup and view all the answers
Given the expression (6𝐱^4 𝐲^2) / (3𝐱 𝐲), what does it simplify to?
Signup and view all the answers
When simplifying (12𝑎^3 𝑏) / (6𝑎^2), what is the result?
Signup and view all the answers
If you divide (24𝐦^4) / (4𝐦), what is the simplified expression?
Signup and view all the answers
What is the simplified form of $(x+3)^3 \times 8^2 \div (y+2)^7$?
Signup and view all the answers
In the expression $(a^2 - 81) \div (z^2 - 3z - 10)$, what is the simplest form?
Signup and view all the answers
What is the simplified result of $7x^2 imes y^{-9} imes z^2 \div (z+4)(y+2)^{14}$?
Signup and view all the answers
In the expression $5(b-6) imes z^2 \div (z^2 - 16)(z+6)$, what is the simplest form?
Signup and view all the answers
What is the simplified form of $7x^{22} imes x^{-9}$?
Signup and view all the answers
Simplify the expression $x^{7} imes x^{-9} imes x$.
Signup and view all the answers
Study Notes
Simplifying Expressions Involving Surds
- To simplify expressions involving surds, reduce all surds to their simplest form.
- Surds with the same value under the root can be added or subtracted.
Simplifying Surd Expressions
- To simplify surd expressions, follow these steps:
- Reduce all surds in the expression to their simplest form.
- Simplify the expression using rules of surds.
Simplifying Algebraic Fractions
- To simplify algebraic fractions, follow these steps:
- Cancel any common terms in the numerator and denominator.
- Use index laws to simplify the expression.
- Cancel any algebra (letter) terms from the numerator and denominator.
Multiplying Algebraic Fractions
- To multiply algebraic fractions, follow these steps:
- Multiply the numerators together.
- Multiply the denominators together.
Simplifying Expressions with Indices
- To simplify expressions with indices, follow these steps:
- Simplify the fractions by factorising expressions and dividing by any common terms.
- Multiply the numerators together and the denominators together.
Dividing Algebraic Fractions
- To divide algebraic fractions, follow these steps:
- Flip the second fraction and then multiply them together.
- Simplify the fractions by factorising any expressions which can be factorised.
- Divide out by any common terms to cancel them.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Practice working out different types of questions involving surds and algebraic fractions with this worksheet. Each section includes a worked example, a question with hints, and practice questions for independent work. Visit the provided link for more resources.
