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Square roots and cube roots

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Rounding errors and estimating

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Adding and subtracting decimals

Methods for multiplication and division

Order of operations: BIDMAS

Types of numbers

Understanding place value

Negative numbers: Add, subtract, multiply, divide

Special types of numbers

Multiples, factors and prime factors

Lowest common multiple and highest common factor

Square roots and cube roots

Writing indices and index laws

Standard form

Explainer Video

Tutor: Bilal

Summary

Square roots and cube roots

In a nutshell

Square roots and cube roots are the inverses of the square and cube operations.

Square roots

The square root of a number, $x$ , is denoted as $\sqrt{x}$ . A square root is defined as follows:

If $x=y^2$ , then $\sqrt{x}=y$ .

In other words, finding the square root of $x$ is the same thing as asking what number becomes $x$ when multiplied by itself?

Key facts to know about square roots

The square root of a number is always defined to be positive.
The square root of a negative number does not exist.

Finding square roots

Square roots can either by found by memorising square numbers, or by using a calculator.

Example 1

What is the square root of $36$ ?

You should know that $6^2=6\times6=36$ . Therefore, $\underline{\sqrt{36}=6}$ .

Example 2

What is the square root of $85$ ?

Use the $\sqrt{}$ button on your calculator:

$\underline{\sqrt{85}=9.219544457...}$

Cube roots

The cube root of a number, $x$ , is denoted as $\sqrt[3]{x}$ . A cube root is defined as follows:

If $x=y^3$ , then $\sqrt[3]{x}=y$ .

In other words, finding the cube root of $x$ is the same as asking what number, when cubed, becomes $x$ ?

Key facts to know about cube roots

You can cube root negative numbers.
The cube root of a negative number is negative.

Finding cube roots

Cube numbers can be very large for even smaller numbers. So, in most cases, you will have to use your calculator to find cube roots.

Example 3

What is the cube root of $512$ ?

$8^3=8\times8\times8=512$ , so $\underline{\sqrt[3]{512}=8}$ .

Example 4

What is the cube root of $-100$ ?

Use the $\sqrt[3]{}$ button on your calculator:

$\underline{\sqrt[3]{-100}=-4.641588834...}$

Learn with Basics

Length:

Unit 1

Square and cube numbers

Jump Ahead

Optional

Unit 2

Square roots and cube roots

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

How do you find the square root or cube root of a number?

You can find square roots and cube roots by either memorising square numbers and cube numbers or by using a calculator.

What is the cube root of a number?

The cube root of a number is a number that cubes (multiplies by itself twice) to give the original number.

What is the square root of a number?

The square root of a number is a number that squares (multiplies by itself) to give the original number.

Home

Maths

Types of numbers

Square roots and cube roots

Videos

Summary

Exercises

Select Lesson

Statistics

Qualitative and quantitative data

Representing data: Graphs and charts

Mean, median, mode and range

Frequency tables

Averages from frequency tables

Averages from grouped frequency tables

Scatter graphs

Probability

Calculating probability

Equal and unequal probabilities

Relative frequency

Listing outcomes

Venn diagrams

Trigonometry

Pythagoras’ theorem

Trigonometric ratios: SOH CAH TOA

Finding missing lengths in a triangle

Finding missing angles in a triangle

Drawing shapes

Transformations

Constructions

Constructing triangles

Lines and angles

Types of angles

Angle rules

Interior and exterior angles

Parallel lines

Measures

Area and perimeter: Triangles and quadrilaterals

Area of compound shapes

Volume of prisms

Properties of shapes

Symmetrical shapes and rotational symmetry

Congruent shapes

Similar shapes

Nets and surface area

Shapes

Quadrilaterals: Types and properties

Triangles and regular polygons: Types and properties

Circles: Area and circumference

3D shapes: Identification and properties

Rates of change

Percentage change

Conversion factors

Imperial units

Solving best buy problems

Reading timetables

Maps and scale drawings

Speed: Formula and units

Density: Formula and units

Proportion

Ratio

Other graphs

Interpreting graphs

Solving simultaneous equations using graphs

Quadratic graphs

Travel graphs: Distance-time graphs

Conversion graphs

Straight line graphs

X and Y coordinates

Straight line graphs

Drawing straight line graphs

Finding the gradient

Equation of a straight line: y = mx + c

Drawing a graph of a linear equation

Estimating values using linear graphs

Formulae and equations

Substituting numbers into an expression

Writing and using formulae

Solving equations

Rearranging formulae

Number patterns and sequences

The nth term

Inequalities: Greater than or less than

Simultaneous equations

Algebraic manipulation

Algebraic notation

Algebraic terms

Simplifying algebraic expressions

Multiplying and dividing algebraic expressions

Single brackets: Expanding and factorising

Expanding double brackets: FOIL and multiplication grid

Fractions, decimals and percentages

Converting between fractions, decimals and percentages

Fractions

Fraction operations: Add, subtract, multiply, divide

Percentages

Rounding: Decimal places and significant figures

Rounding errors and estimating

Number calculations

Ordering numbers: Whole numbers and decimals

Addition and subtraction using the column method

Multiplying and dividing by powers of 10

Adding and subtracting decimals

Methods for multiplication and division

Order of operations: BIDMAS

Types of numbers

Understanding place value

Negative numbers: Add, subtract, multiply, divide

Special types of numbers

Multiples, factors and prime factors

Lowest common multiple and highest common factor

Square roots and cube roots

Writing indices and index laws

Standard form

Explainer Video

Tutor: Bilal

Summary

Square roots and cube roots

In a nutshell

Square roots and cube roots are the inverses of the square and cube operations.

Square roots

The square root of a number, $x$ , is denoted as $\sqrt{x}$ . A square root is defined as follows:

If $x=y^2$ , then $\sqrt{x}=y$ .

In other words, finding the square root of $x$ is the same thing as asking what number becomes $x$ when multiplied by itself?

Key facts to know about square roots

The square root of a number is always defined to be positive.
The square root of a negative number does not exist.

Finding square roots

Square roots can either by found by memorising square numbers, or by using a calculator.

Example 1

What is the square root of $36$ ?

You should know that $6^2=6\times6=36$ . Therefore, $\underline{\sqrt{36}=6}$ .

Example 2

What is the square root of $85$ ?

Use the $\sqrt{}$ button on your calculator:

$\underline{\sqrt{85}=9.219544457...}$

Cube roots

The cube root of a number, $x$ , is denoted as $\sqrt[3]{x}$ . A cube root is defined as follows:

If $x=y^3$ , then $\sqrt[3]{x}=y$ .

In other words, finding the cube root of $x$ is the same as asking what number, when cubed, becomes $x$ ?

Key facts to know about cube roots

You can cube root negative numbers.
The cube root of a negative number is negative.

Finding cube roots

Cube numbers can be very large for even smaller numbers. So, in most cases, you will have to use your calculator to find cube roots.

Example 3

What is the cube root of $512$ ?

$8^3=8\times8\times8=512$ , so $\underline{\sqrt[3]{512}=8}$ .

Example 4

What is the cube root of $-100$ ?

Use the $\sqrt[3]{}$ button on your calculator:

$\underline{\sqrt[3]{-100}=-4.641588834...}$

Learn with Basics

Length:

Unit 1

Square and cube numbers

Jump Ahead

Optional

Unit 2

Square roots and cube roots

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

How do you find the square root or cube root of a number?

You can find square roots and cube roots by either memorising square numbers and cube numbers or by using a calculator.

What is the cube root of a number?

The cube root of a number is a number that cubes (multiplies by itself twice) to give the original number.

What is the square root of a number?

The square root of a number is a number that squares (multiplies by itself) to give the original number.