Rationalising the Denominator 4

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Year 8

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Rationalising the Denominator

Rationalising the Denominator 4

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Question 1 of 6

Rationalise the denominator:

$(sqrt6 + sqrt3)/(2sqrt6)$

1. $4sqrt2$
2. $sqrt2/4$
3. $sqrt2$
4. $(2+sqrt2)/4$

Question 2 of 6

Rationalise the denominator:

$(sqrt10 – sqrt5)/(5sqrt10)$

1. $sqrt2/10$
2. $sqrt20$
3. $(2-sqrt2)/10$
4. $20sqrt2$

Question 3 of 6

Rationalise the denominator:

$2/(3-sqrt2)$

1. $(5-2sqrt2)/7$
2. $(6-2sqrt2)/5$
3. $(3+sqrt2)/3$
4. $(6+2sqrt2)/7$

Question 4 of 6

Rationalise the denominator:

$2/(sqrt3-1)$

1. $(2sqrt3+2)/(sqrt6-1)$
2. $(sqrt3+1)/4$
3. $2sqrt3+2$
4. $sqrt3+1$

Question 5 of 6

Rationalise the denominator:

$(sqrt6+1)/(sqrt6+sqrt2)$

1. $(3-sqrt3+sqrt6-2sqrt5)/5$
2. $(6-sqrt3+2sqrt6-sqrt5)/5$
3. $(5+sqrt3-sqrt2)/4$
4. $(6-2sqrt3+sqrt6-sqrt2)/4$

Question 6 of 6

Rationalise the denominator:

$(sqrt5-sqrt2)/(sqrt5+sqrt2)$

1. $(7-2sqrt10)/3$
2. $(5+4sqrt2)/3$
3. $(4-sqrt10)/2$
4. $(7-2sqrt5)/4$

$(sqrt6 + sqrt3)/(2sqrt6)$	$=$	$(sqrt6 + sqrt3)/(2sqrt6) xx color(crimson)((sqrt6)/(sqrt6))$

	$=$	$((sqrt6 + sqrt3) xx sqrt6)/(2 xx (sqrt6 xx sqrt6))$
	$=$	$(sqrt6 xx sqrt6+ sqrt3 xx sqrt6)/(2 xx (sqrt6 xx sqrt6)$	Apply Distributive Property of Multiplication
	$=$	$(sqrt36 + sqrt18)/(2 xx sqrt36)$	Apply the Multiplication Property
	$=$	$(6+3sqrt2)/12$	$sqrt(36) = 6$ and $sqrt(18) = 3sqrt2$
	$=$	$(2+sqrt2)/4$	Simplify

$(sqrt10 – sqrt5)/(5sqrt10)$	$=$	$(sqrt10 – sqrt5)/(5sqrt10) xx color(crimson)((sqrt10)/(sqrt10))$
	$=$	$((sqrt10 – sqrt5) xx sqrt10)/(5 xx (sqrt10 xx sqrt10))$
	$=$	$(sqrt10 xx sqrt10- sqrt5 xx sqrt10)/(5 xx (sqrt10 xx sqrt10)$	Apply Distributive Property of Multiplication
	$=$	$(sqrt100 – sqrt50)/(5 xx sqrt100)$	Apply the Multiplication Property
	$=$	$(10 – 5sqrt2)/(50)$	$sqrt(100) = 10$ and $sqrt(50) = 5sqrt2$
	$=$	$(2-sqrt2)/10$	Simplify

$2/(3-sqrt2)$	$=$	$2/(3-sqrt2) xx$ $(3+sqrt2)/(3+sqrt2)$

	$=$	$(2 xx (3+sqrt2))/((3-sqrt2) xx (3+sqrt2))$

	$=$	$(6+2sqrt2)/(9-2)$	Apply Multiplication Property

	$=$	$(6+2sqrt2)/(9-2)$	Apply Multiplication Property

	$=$	$(6+2sqrt2)/7$

$2/(sqrt3-1)$	$=$	$2/(sqrt3-1) xx$ $(sqrt3+1)/(sqrt3+1)$

	$=$	$(2 xx (sqrt3+1))/((sqrt3-1) xx (sqrt3+1))$

	$=$	$(2sqrt3+2)/(sqrt9+sqrt3-sqrt3-1)$	Expand the brackets

	$=$	$(2sqrt3+2)/(3-1)$	$sqrt(9) = 3$

	$=$	$(2sqrt3+2)/2$

	$=$	$sqrt3+1$

$(sqrt6+1)/(sqrt6+sqrt2)$	$=$	$(sqrt6+1)/(sqrt6+sqrt2) xx$ $(sqrt6-sqrt2)/(sqrt6-sqrt2)$

	$=$	$((sqrt6+1)(sqrt6-sqrt2))/((sqrt6+sqrt2)(sqrt6-sqrt2))$

	$=$	$(6-sqrt12+sqrt6-sqrt2)/(6-2)$	Expand the brackets

	$=$	$(6-2sqrt3+sqrt6-sqrt2)/4$

Rationalising the Denominator 4

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Quiz summary

Information

1. Question

Excellent!

Division Property of Square Roots

2. Question

Excellent!

Division Property of Square Roots

3. Question

Hint

Great Work!

4. Question

Hint

Great Work!

5. Question

Hint

Excellent!

6. Question

Hint

Well Done!

Quizzes

$(sqrt5-sqrt2)/(sqrt5+sqrt2)$	$=$	$(sqrt5-sqrt2)/(sqrt5+sqrt2) xx$ $(sqrt5-sqrt2)/(sqrt5-sqrt2)$

	$=$	$((sqrt5-sqrt2)(sqrt5-sqrt2))/((sqrt5+sqrt2)(sqrt5-sqrt2))$

	$=$	$(5-sqrt10-sqrt10+2)/(5-2)$	Expand the brackets

	$=$	$(7-2sqrt10)/3$