What is a square root of a number?

A square root of a number is a value that, when squared , gives the original number . E.g. 3 is the square root of 9 because 3 2 = 3 x 3 = 9.

True or False? Cube roots of negative numbers do not exist .

False. The cube root of a negative number will also be a negative number . For example, -5 is a cube root of -125.

IGCSEMathsEdexcelMaths AFoundationFlashcards1. Numbers & the Number SystemPowers, Roots & Standard Form

Powers, Roots & Standard Form (Edexcel IGCSE Maths A: Foundation): Flashcards

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What is a square root of a number?

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What is a square root of a number?
A square root of a number is a value that, when squared, gives the original number.
E.g. 3 is the square root of 9 because 3² = 3 x 3 = 9.
True or False?
Every positive number has two square roots.
True.
Every positive number has two square roots, one positive and one negative.
E.g. $\sqrt{64} = 8$ and $- 8$
True or False?
Cube roots of negative numbers do not exist.
False.
The cube root of a negative number will also be a negative number.
For example, -5 is a cube root of -125.
Define the term reciprocal.
The reciprocal of a number is the number that you multiply it by to get 1.
For example, $\frac{2}{3}$ is the reciprocal of $\frac{3}{2}$ .
How do I estimate a root, e.g. the square root of 27?
You can estimate the root of a number by finding the closest integer roots either side of it.
E.g. To find $\sqrt{27}$
$\sqrt{25} = 5$ and $\sqrt{36} = 6$
So $\sqrt{27}$ is between $5$ and $6$
Complete the two index laws below by filling in the missing indices:
$a^{m} \times a^{n} = a^{______}$
$a^{m} \div a^{n} = a^{______}$
The completed laws are:
$a^{m} \times a^{n} = a^{m + n}$
$a^{m} \div a^{n} = a^{m - n}$
Multiplying adds the indices, and dividing subtracts them.
How do you simplify a power that is raised to another power, such as ${(14^{3})}^{2}$ ?
Multiply the two indices: ${(a^{m})}^{n} = a^{m n}$ .
So ${(14^{3})}^{2} = 14^{3 \times 2} = 14^{6}$ .
What is the value of a number raised to the power of $0$ ?
Any non-zero number raised to the power of $0$ is $1$ .
The base makes no difference: $8^{0} = 1$ , $100^{0} = 1$ and ${(- 3)}^{0} = 1$ .
What does a negative index tell you to do, for example in $2^{- 4}$ ?
A negative index means the reciprocal of the positive power: $a^{- n} = \frac{1}{a^{n}}$ .
So $2^{- 4} = \frac{1}{2^{4}} = \frac{1}{16}$ .
How do you expand a product or a fraction that is raised to a power?
Apply the power to each number separately: ${(a b)}^{n} = a^{n} b^{n}$ and ${(\frac{a}{b})}^{n} = \frac{a^{n}}{b^{n}}$ .
For example, ${(\frac{3}{4})}^{2} = \frac{3^{2}}{4^{2}} = \frac{9}{16}$ .
True or False?
The index laws can be used to simplify $2^{5} \times 4^{3}$ .
True.
Although the two bases look different, $4 = 2^{2}$ , so the whole expression can be written with base $2$ :
$2^{5} \times {(2^{2})}^{3} = 2^{5} \times 2^{6} = 2^{11}$
The index laws only work once the bases are the same.
How do you find the value of $x$ in the equation $6^{10 + x} = 6^{2}$ ?
Since both sides have the same base, their indices must be equal, so $10 + x = 2$ .
Subtracting $10$ from both sides gives $x = - 8$ .
What does a number written in standard form look like?
A number in standard form looks like $a \times 10^{n}$ , e.g. $5.2 \times 10^{3}$ .
It is a number between 1 and 10 multiplied by a power of ten.
When a number is written in standard form $a \times 10^{n}$ , which values can $a$ be?
For $a \times 10^{n}$ , $a$ is at least 1 and less than 10, $1 \leq a < 10$ .
This means there is one non-zero digit before the decimal point.
True or False?
When a number is written in standard form $a \times 10^{n}$ , $n$ can be a fraction.
False.
For a number written in standard form, $a \times 10^{n}$ , the value $n$ must be an integer.
It can be zero, positive or negative.
When a value between 0 and 1, is written in standard form $a \times 10^{n}$ , what type of number will $n$ be?
If a value is between 0 and 1 then when it is written in standard form, $n$ will be a negative integer.
E.g. 0.083 would be written as 8.3 x 10^-2.

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