MYP Standard Mathematics Topic Radicals Revision Notes

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MYP Standard Mathematics Topic Radicals Revision Notes | RevisionDojo

Radicals (also called surds) are a way of writing many irrational numbers exactly.
In this topic you will learn to recognize rational and irrational numbers, use key rules of radicals, simplify surd expressions, and estimate surds without a calculator.

What Radicals Represent

Many measurements and calculations produce numbers like $\sqrt{2}$ or $\sqrt{5}$.
These cannot be written exactly as terminating or repeating decimals, but they can be written exactly using surd notation.

Definition

Radical (surd)

An irrational number written in radical form, such as $\sqrt{2}$ or $2\sqrt{3}$.

Definition

Radical sign

The symbol $\sqrt{\;}$ used to indicate a root.

Definition

Radicand

The number or expression inside the radical sign, for example the $5$ in $\sqrt{5}$.

A square root of a positive number $x$ is a number which, when multiplied by itself, gives $x$.
Any positive number has two square roots, one positive and one negative.

Example

$25$ has square roots $5$ and $-5$.

In most school mathematics, "the square root of $x$" means the principal square root, the positive one, written $\sqrt{x}$.
The negative square root is written $-\sqrt{x}$.

Note

Using the radical symbol is the only way to write many square roots exactly.
For example, $\sqrt{5}$ cannot be written as a terminating or repeating decimal.

Rational And Irrational Numbers Describe Different Decimal Behaviors

A rational number is a number that can be written as a fraction $\frac{p}{q}$ where $p,q\in\mathbb{Z}$ and $q\neq 0$.
1. Rational numbers have decimal expansions that terminate (end) or repeat.
An irrational number cannot be written as $\frac{p}{q}$.
1. Irrational numbers have decimal expansions that do not terminate and do not repeat (like $\pi$).
2. Many square roots are irrational.
3. For example, $\sqrt{2}$ is irrational.

Common Mistake

A number can be written with a radical sign and still be rational.
For example, $\sqrt{9}=3$, so it is rational.

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MYP Standard Mathematics Radicals Notes

What Radicals Represent

Rational And Irrational Numbers Describe Different Decimal Behaviors

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Excepteur sint occaecat cupidatat non proident

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What Radicals Represent

Rational And Irrational Numbers Describe Different Decimal Behaviors

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Number and Algebra Foundations7 subtopics

Coordinate Geometry and Linear Modelling5 subtopics

Functions and Quadratic Relationships4 subtopics

Sets, Logic and Probability4 subtopics

Geometry of Shapes, Surface Area and Volume3 subtopics

Statistical Measures and Data Representation3 subtopics

Right Triangles and Circle Geometry3 subtopics

Sequences, Formulae and Proportional Reasoning3 subtopics

Sampling Methods and Bivariate Data2 subtopics

MYP Standard Mathematics Radicals Notes

Number and Algebra Foundations7 subtopics

Coordinate Geometry and Linear Modelling5 subtopics

Functions and Quadratic Relationships4 subtopics

Sets, Logic and Probability4 subtopics

Geometry of Shapes, Surface Area and Volume3 subtopics

Statistical Measures and Data Representation3 subtopics

Right Triangles and Circle Geometry3 subtopics

Sequences, Formulae and Proportional Reasoning3 subtopics

Sampling Methods and Bivariate Data2 subtopics

What Radicals Represent

Rational And Irrational Numbers Describe Different Decimal Behaviors

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account

What Radicals Represent

Rational And Irrational Numbers Describe Different Decimal Behaviors

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

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