Rationalising the Denominator 2

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Year 8

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Rationalising the Denominator

Rationalising the Denominator 2

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Question 1 of 6

Rationalise the denominator:

\frac{1}{\sqrt{5}}

$1/(sqrt5)$

1. $5 - \sqrt{5}$ $5-sqrt5$
2. $5 + \sqrt{5}$ $5+sqrt5$
3. $\frac{5}{\sqrt{5}}$ $5/sqrt5$
4. $\frac{\sqrt{5}}{5}$ $sqrt5 /5$

Question 2 of 6

Rationalise the denominator:

\frac{3}{\sqrt{2}}

$3/(sqrt2)$

1. $2 - 3 \sqrt{2}$ $2-3sqrt2$
2. $2 + 3 \sqrt{2}$ $2+3sqrt2$
3. $\frac{6}{\sqrt{2}}$ $6/sqrt2$
4. $\frac{3 \sqrt{2}}{2}$ $(3sqrt2) /2$

Question 3 of 6

Rationalise the denominator:

\frac{\sqrt{7}}{\sqrt{3}}

$sqrt7/sqrt3$

1. $\frac{\sqrt{21}}{3}$ $(sqrt21)/3$
2. $\frac{\sqrt{18}}{3}$ $(sqrt18)/3$
3. $\frac{2 \sqrt{21}}{3}$ $(2sqrt21)/3$
4. $\frac{4 \sqrt{2}}{3}$ $(4sqrt2)/3$

Question 4 of 6

Rationalise the denominator:

\frac{\sqrt{10 x}}{\sqrt{6}}

$sqrt(10x)/sqrt6$

1. $\frac{\sqrt{15 x}}{3}$ $(sqrt(15x))/3$
2. $\frac{\sqrt{15 x}}{6}$ $(sqrt(15x))/6$
3. $\frac{\sqrt{45 x}}{3}$ $(sqrt(45x))/3$
4. $\sqrt{45 x}$ $sqrt(45x)$

Question 5 of 6

Rationalise the denominator:

\frac{\sqrt{3} - 1}{6 \sqrt{3}}

$(sqrt3-1)/(6sqrt3)$

1. $\frac{3 - \sqrt{3}}{18}$ $(3-sqrt3)/18$
2. $\frac{\sqrt{3} - 3}{6}$ $(sqrt3-3)/6$
3. $\frac{1 - \sqrt{3}}{9}$ $(1-sqrt3)/9$
4. $3 - 6 \sqrt{3}$ $3-6sqrt3$

Question 6 of 6

Rationalise the denominator:

$(sqrt5-sqrt3)/(sqrt5+sqrt3)$

1. $1-sqrt15$
2. $(sqrt10-2sqrt15+sqrt6)/(sqrt10-sqrt6)$
3. $4-sqrt15$
4. $1/(4+sqrt15)$

$\frac{1}{\sqrt{5}}$ $1/(sqrt5)$	$=$ $=$	$\frac{1}{\sqrt{5}} \times$ $1/(sqrt5) xx$ $\frac{\sqrt{5}}{\sqrt{5}}$ $(sqrt5)/(sqrt5)$

	$=$ $=$	$\frac{\sqrt{5}}{\sqrt{5} \times \sqrt{5}}$ $(sqrt5)/(sqrt5 xx sqrt5)$

	$=$ $=$	$\frac{\sqrt{5}}{\sqrt{25}}$ $(sqrt5)/(sqrt25)$	Apply Multiplication Property

	$=$ $=$	$\frac{\sqrt{5}}{5}$ $(sqrt5)/5$	$\sqrt{25} = 5$ $sqrt(25) = 5$

$\frac{3}{\sqrt{2}}$ $3/(sqrt2)$	$=$ $=$	$\frac{3}{\sqrt{2}} \times$ $3/(sqrt2) xx$ $\frac{\sqrt{2}}{\sqrt{2}}$ $(sqrt2)/(sqrt2)$

	$=$ $=$	$\frac{3 \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}}$ $(3 xx sqrt2)/(sqrt2 xx sqrt2)$

	$=$ $=$	$\frac{3 \sqrt{2}}{\sqrt{4}}$ $(3sqrt2)/(sqrt4)$	Apply Multiplication Property

	$=$ $=$	$\frac{3 \sqrt{2}}{2}$ $(3sqrt2)/2$	$\sqrt{4} = 2$ $sqrt(4) = 2$

$\frac{\sqrt{7}}{\sqrt{3}}$ $sqrt7/sqrt3$	$=$ $=$	$\frac{\sqrt{7}}{\sqrt{3}} \times$ $sqrt7/sqrt3 xx$ $\frac{\sqrt{3}}{\sqrt{3}}$ $(sqrt3)/(sqrt3)$

	$=$ $=$	$\frac{\sqrt{7} \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}$ $(sqrt7 xx sqrt3)/(sqrt3 xx sqrt3)$

	$=$ $=$	$\frac{\sqrt{21}}{3}$ $(sqrt21)/3$	Apply Multiplication Property

$\frac{\sqrt{10 x}}{\sqrt{6}}$ $sqrt(10x)/sqrt6$	$=$ $=$	$\frac{\sqrt{10 x}}{\sqrt{6}} \times$ $sqrt(10x)/sqrt6 xx$ $\frac{\sqrt{6}}{\sqrt{6}}$ $(sqrt6)/(sqrt6)$

	$=$ $=$	$\frac{\sqrt{10 x} \times \sqrt{6}}{\sqrt{6} \times \sqrt{6}}$ $(sqrt(10x) xx sqrt6)/(sqrt6 xx sqrt6)$

	$=$ $=$	$\frac{\sqrt{60 x}}{6}$ $(sqrt(60x))/6$	Apply Multiplication Property

	$=$ $=$	$\frac{\sqrt{4 \times 15 x}}{6}$ $(sqrt(4xx15x))/6$	Simplify the numerator

	$=$ $=$	$\frac{2 \sqrt{15 x}}{6}$ $(2sqrt(15x))/6$

	$=$ $=$	$\frac{\sqrt{15 x}}{3}$ $(sqrt(15x))/3$	Reduce to lowest terms

$\frac{\sqrt{3} - 1}{6 \sqrt{3}}$ $(sqrt3-1)/(6sqrt3)$	$=$ $=$	$\frac{\sqrt{3} - 1}{6 \sqrt{3}} \times$ $(sqrt3-1)/(6sqrt3) xx$ $\frac{\sqrt{3}}{\sqrt{3}}$ $(sqrt3)/(sqrt3)$

	$=$ $=$	$\frac{\sqrt{3} \times (\sqrt{3} - 1)}{6 \sqrt{3} \times \sqrt{3}}$ $(sqrt3 xx (sqrt3-1))/(6sqrt3 xx sqrt3)$

	$=$	$(3-sqrt3)/18$	Apply Multiplication Property

Rationalising the Denominator 2

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2. Question

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Quizzes

$(sqrt5-sqrt3)/(sqrt5+sqrt3)$	$=$	$(sqrt5-sqrt3)/(sqrt5+sqrt3) xx$ $(sqrt5-sqrt3)/(sqrt5-sqrt3)$

	$=$	$((sqrt5-sqrt3)(sqrt5-sqrt3))/((sqrt5+sqrt3)(sqrt5-sqrt3))$

	$=$	$(sqrt25-sqrt15-sqrt15+sqrt9)/(sqrt25-sqrt15+sqrt15-sqrt9)$	Expand the brackets

	$=$	$(5-2sqrt15+3)/(5-3)$	$sqrt(25)=5$ and $sqrt(9) = 3$
	$=$	$(8-2sqrt15)/2$
	$=$	$4-sqrt15$