## 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.