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 .

IGCSEMaths A: HigherEdexcelFlashcards

Surds (Edexcel IGCSE Maths A)

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FrontSimplifying Surds
Define the term surd.

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Cards in this collection (16)

Define the term surd.
A surd is a square root of a non-square positive integer.
Examples include $\sqrt{7}, \sqrt{12}, \sqrt{99}$ .
Simplify $\sqrt{a} \times \sqrt{b}$ .
$\sqrt{a} \times \sqrt{b}$ simplifies to $\sqrt{a \times b}$ .
Simplify $\frac{\sqrt{a}}{\sqrt{b}}$ .
$\frac{\sqrt{a}}{\sqrt{b}}$ simplifies to $\sqrt{\frac{a}{b}}$ .
Simplify ${(\sqrt{a})}^{2}$ .
${(\sqrt{a})}^{2}$ simplifies to $a$ .
True or False?
$\sqrt{2} + \sqrt{3}$ simplifies to $\sqrt{5}$ .
False.
$\sqrt{2} + \sqrt{3}$ does not simplify to $\sqrt{5}$ . The surds need to be the same in order to add or subtract.
How can you simplify a surd such as $\sqrt{8}$ ?
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.
For example, $\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2 \sqrt{2}$
How do you add or subtract two surds?
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, $\sqrt{8} + \sqrt{18} = 2 \sqrt{2} + 3 \sqrt{2} = 5 \sqrt{2}$
How do you expand two brackets with expressions containing surds?
To expand two brackets with expressions containing surds, you multiply each term in one bracket by each term in the other bracket. And use the rules: $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$ and $\sqrt{a} \times \sqrt{a} = a$ .
True or False?
${(a + \sqrt{b})}^{2} = a^{2} + b$ .
False.
${(a + \sqrt{b})}^{2} \neq a^{2} + b$ . You need to expand using double brackets, $(a + \sqrt{b}) (a + \sqrt{b})$ . This expands and simplifies to $a^{2} + b + 2 a \sqrt{b}$ .
Simplify $(a + \sqrt{b}) (a - \sqrt{b})$ .
$(a + \sqrt{b}) (a - \sqrt{b})$ simplifies to $a^{2} - b$ . 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.
What should you multiply the numerator and the denominator of $\frac{3}{\sqrt{2}}$ by to rationalise the denominator?
To rationalise the denominator of $\frac{3}{\sqrt{2}}$ , you should multiply the numerator and the denominator by $\sqrt{2}$ .
What should you multiply the numerator and the denominator of $\frac{3}{5 - \sqrt{2}}$ by to rationalise the denominator?
To rationalise the denominator of $\frac{3}{5 - \sqrt{2}}$ , you should multiply the numerator and the denominator by $5 + \sqrt{2}$ .
True or False?
Multiplying the numerator and denominator of $\frac{2 + \sqrt{3}}{3 - \sqrt{5}}$ by $2 - \sqrt{3}$ will rationalise the denominator.
False.
Multiplying the numerator and denominator of $\frac{2 + \sqrt{3}}{3 - \sqrt{5}}$ by $2 - \sqrt{3}$ will not rationalise the denominator. You should use $3 + \sqrt{5}$ instead.
True or False?
Multiplying the numerator and denominator of $\frac{5}{\sqrt{7} - \sqrt{2}}$ by $\sqrt{7} - \sqrt{2}$ will rationalise the denominator.
False.
Multiplying the numerator and denominator of $\frac{5}{\sqrt{7} - \sqrt{2}}$ by $\sqrt{7} - \sqrt{2}$ will not rationalise the denominator. You should use $\sqrt{7} + \sqrt{2}$ instead.
To rationalise the denominator $(p + \sqrt{q})$ , you multiply the numerator and the denominator by what?
To rationalise the denominator $(p + \sqrt{q})$ , you multiply the numerator and the denominator by $(p - \sqrt{q})$ .

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