What is a surd?
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What is a surd?
A surd is a square root of a non-square positive integer.
It is an irrational number.
Examples include .
Simplify .
simplifies to .
Simplify .
simplifies to .
Simplify .
simplifies to .
True or False?
simplifies to .
False.
does not simplify to .
The surds need to be of the same type (e.g. all multiple of ) to be able to add or subtract.
How can you simplify a surd such as ?
To simplify a surd, write the number as a product involving a square number.
Split the surd into the product of two surds, one of which should just become an integer.
E.g. .
How do you add or subtract two surds?
E.g. .
To add or subtract two surds, simplify both surds so that they are both multiples of the same surd.
You can then add or subtract by collecting like terms.
For example,
How do you expand two brackets with expressions containing surds?
E.g.
To expand two brackets with expressions containing surds, you multiply each term in one bracket by each term in the other bracket.
E.g.
True or False?
.
False.
.
You need to expand using double brackets, .
This expands and simplifies to .
Simplify .
simplifies to .
This is an example of the difference of two squares.
State what is meant by rationalising the denominator.
Rationalising the denominator changes a fraction with surds in the denominator into an equivalent fraction where there are no surds in the denominator.
E.g. The fraction becomes .
What should you multiply the numerator and the denominator of by to rationalise the denominator?
To rationalise the denominator of , you should multiply the numerator and the denominator by .
What should you multiply the numerator and the denominator of by to rationalise the denominator?
To rationalise the denominator of , you should multiply the numerator and the denominator by .
True or False?
Multiplying the numerator and denominator of by will rationalise the denominator.
False.
Multiplying the numerator and denominator of by will not rationalise the denominator.
You need to multiply by instead.
The multiplier should contain the same terms as the denominator but with the sign between them inverted.
True or False?
Multiplying the numerator and denominator of by will rationalise the denominator.
False.
Multiplying the numerator and denominator of by will not rationalise the denominator.
You should multiply by instead.
The sign in between the two terms should be inverted.
To rationalise a denominator , you multiply the numerator and the denominator by what expression?
To rationalise a denominator , you multiply the numerator and the denominator by .