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# GCSE Maths Algebra Expressions Involving Surds and Algebraic Fractions Worksheet

Created by
@SmarterTangent

### What is the simplified form of √75𝑎𝑎 + 8√3 − 9√3𝑎𝑎?

• 8√3 − 9𝑎𝑎
• 8√3 − 4√3𝑎𝑎
• 8√3 − 9√3𝑎𝑎 (correct)
• 8√3 − 9𝑎
• ### What does √𝟕𝟕𝟕 mean when simplified?

• 5√3 (correct)
• 5√7
• 25√3
• 35

• +5 (correct)
• 5 (correct)
• -5
• -25

### In the expression √75𝑎𝑎 + 8√3 − 9√3𝑎𝑎, what does the term √75 represent?

<p>5√3a</p> Signup and view all the answers

### What happens when you divide 16𝒂^2 𝒃^3 by 8𝒂 𝒃?

<p>2𝒂 𝒃^2</p> Signup and view all the answers

### After simplifying 5𝑐𝑐^8 / 4𝑐𝑐^2, what is the result?

<p>5𝑐𝑐^6 / 4</p> Signup and view all the answers

### What is the result of dividing 9𝑎^3 𝑏^3 by 9𝑎^4 𝑏^3?

<p>𝑎𝑎𝑎𝑎</p> Signup and view all the answers

### Given the expression (6𝐱^4 𝐲^2) / (3𝐱 𝐲), what does it simplify to?

<p>2𝐱^3 𝐲</p> Signup and view all the answers

### When simplifying (12𝑎^3 𝑏) / (6𝑎^2), what is the result?

<p>2𝑎 𝑏</p> Signup and view all the answers

### If you divide (24𝐦^4) / (4𝐦), what is the simplified expression?

<p>$6m$</p> Signup and view all the answers

### What is the simplified form of $(x+3)^3 \times 8^2 \div (y+2)^7$?

<p>$(x+3)^3 \times 64 \div (y+2)^7$</p> Signup and view all the answers

### In the expression $(a^2 - 81) \div (z^2 - 3z - 10)$, what is the simplest form?

<p>$(a+9)(a-9) \div z^2 - 3z -10$</p> Signup and view all the answers

### What is the simplified result of $7x^2 imes y^{-9} imes z^2 \div (z+4)(y+2)^{14}$?

<p>$7x^2y^{-9}z^2 \div (z+4)(y+2)^{14}$</p> 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?

<p>$5(b-6)z^2 \div (z-4)(z+6)$</p> Signup and view all the answers

### What is the simplified form of $7x^{22} imes x^{-9}$?

<p>$7x^{31}$</p> Signup and view all the answers

### Simplify the expression $x^{7} imes x^{-9} imes x$.

<p>$x^{17}$</p> 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.

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## 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.

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