Rationalising the Denominator 1

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Year 8

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Rationalising the Denominator

Rationalising the Denominator 1

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Question 1 of 5

Rationalise the denominator:

\frac{5}{4 \sqrt{3}}

$5/(4sqrt3)$

1. $\frac{5 \sqrt{3}}{12}$ $(5sqrt3)/12$
2. $\frac{5}{12 \sqrt{3}}$ $5/(12sqrt3)$
3. $5 \sqrt{3} - 12$ $5sqrt3-12$
4. $\frac{15}{4 \sqrt{3}}$ $15/(4sqrt3)$

Question 2 of 5

Rationalise the denominator:

\frac{\sqrt{5 x^{2}}}{\sqrt{8}}

$sqrt(5x^2)/sqrt8$

1. $\frac{x \sqrt{10}}{4}$ $(xsqrt10)/4$
2. $\frac{2 x \sqrt{5}}{5}$ $(2xsqrt5)/5$
3. $\frac{\sqrt{10 x}}{8}$ $(sqrt(10x))/8$
4. $\frac{3 x \sqrt{8}}{4}$ $(3xsqrt8)/4$

Question 3 of 5

Rationalise the denominator:

\frac{8 \sqrt{5}}{3 \sqrt{2}}

$(8sqrt5)/(3sqrt2)$

1. $\frac{40}{3 \sqrt{10}}$ $40/(3sqrt10)$
2. $\frac{4 \sqrt{7}}{3}$ $(4sqrt7)/3$
3. $\frac{4 \sqrt{10}}{3}$ $(4sqrt10)/3$
4. $24 \sqrt{10} - 18$ $24sqrt10-18$

Question 4 of 5

Rationalise the denominator:

$(sqrt3+1)/(sqrt7)$

1. $(sqrt21+sqrt7)/(7)$
2. $(sqrt28)/(7)$
3. $(3+sqrt3)/sqrt21$
4. $(sqrt21+1)/(7)$

Question 5 of 5

Rationalise the denominator:

$1/(5+sqrt3)+1/(5-sqrt3)$

1. $10/22$
2. $2/10$
3. $2/22$
4. $(5+2sqrt3)/22$

$\frac{5}{4 \sqrt{3}}$ $5/(4sqrt3)$	$=$ $=$	$\frac{5}{4 \sqrt{3}} \times$ $5/(4sqrt3) xx$ $\frac{\sqrt{3}}{\sqrt{3}}$ $(sqrt3)/(sqrt3)$

	$=$ $=$	$\frac{5 \times \sqrt{3}}{4 \sqrt{3} \times \sqrt{3}}$ $(5 xx sqrt3)/(4sqrt3 xx sqrt3)$

	$=$ $=$	$\frac{5 \sqrt{3}}{4 \sqrt{9}}$ $(5sqrt3)/(4sqrt9)$	Apply Multiplication Property

	$=$ $=$	$\frac{5 \sqrt{3}}{4 \times 3}$ $(5sqrt3)/(4 xx 3)$	$\sqrt{9} = 3$ $sqrt(9) = 3$

	$=$ $=$	$\frac{5 \sqrt{3}}{12}$ $(5sqrt3)/12$

$\frac{\sqrt{5 x^{2}}}{\sqrt{8}}$ $sqrt(5x^2)/sqrt8$	$=$ $=$	$\frac{\sqrt{5 x^{2}}}{\sqrt{8}} \times$ $sqrt(5x^2)/sqrt8 xx$ $\frac{\sqrt{8}}{\sqrt{8}}$ $(sqrt8)/(sqrt8)$

	$=$ $=$	$\frac{\sqrt{5 x^{2}} \times \sqrt{8}}{\sqrt{8} \times \sqrt{8}}$ $(sqrt(5x^2) xx sqrt8)/(sqrt8 xx sqrt8)$

	$=$ $=$	$\frac{\sqrt{40 x^{2}}}{8}$ $(sqrt(40x^2))/8$	Apply Multiplication Property

	$=$ $=$	$\frac{\sqrt{4 x^{2} \times 10}}{8}$ $(sqrt(4x^2xx10))/8$	Simplify the numerator

	$=$ $=$	$\frac{2 x \sqrt{10}}{8}$ $(2xsqrt10)/8$

	$=$ $=$	$\frac{x \sqrt{10}}{4}$ $(xsqrt10)/4$	Reduce to lowest terms

$\frac{8 \sqrt{5}}{3 \sqrt{2}}$ $(8sqrt5)/(3sqrt2)$	$=$ $=$	$\frac{8 \sqrt{5}}{3 \sqrt{2}} \times$ $(8sqrt5)/(3sqrt2) xx$ $(sqrt2)/(sqrt2)$

	$=$	$(8sqrt5 xx sqrt2)/(3sqrt2 xx sqrt2)$

	$=$	$(8sqrt10)/(3sqrt4)$	Apply Multiplication Property

	$=$	$(8sqrt10)/(3 xx 2)$	$sqrt(4) = 2$

	$=$	$(8sqrt10)/6$

	$=$	$(4sqrt10)/3$	Simplify the fraction

$(sqrt3+1)/(sqrt7)$	$=$	$(sqrt3+1)/(sqrt7) xx$ $(sqrt7)/(sqrt7)$

	$=$	$((sqrt3+1) xx sqrt7)/(sqrt7 xx sqrt7)$

	$=$	$(sqrt7 xx sqrt3 + sqrt7 xx 1)/(sqrt7 xx sqrt7)$	Apply Distributive Property

	$=$	$(sqrt21+sqrt7)/(sqrt49)$	Apply Multiplication Property

	$=$	$(sqrt21+sqrt7)/(7)$	$sqrt(49) = 7$

$1/(5+sqrt3)+1/(5-sqrt3)$	$=$	$(1(5+sqrt3)+1(5-sqrt3))/((5+sqrt3)(5-sqrt3))$

	$=$	$(5+sqrt3+5-sqrt3)/(25-5sqrt3+5sqrt3-sqrt3 xx sqrt3)$	Expand the brackets

	$=$	$(10)/(25-sqrt3 xx sqrt3)$

	$=$	$(10)/(25-3)$	$sqrt(3) xx sqrt(3) = 3$

	$=$	$(10)/22$

Rationalising the Denominator 1

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