What is a rational number ?

A rational number is a number that can be written as a ratio.

A rational number is a number that cannot be written as a fraction.

A rational number cannot be a repeating decimal.

Simplify and then evaluate: 3 2 − 3 18 = 3\sqrt{2}\ -\ 3\sqrt{18}= 3 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 3 1 8 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> =

− 6 2 -6\sqrt{2} − 6 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

− 4 8 -4\sqrt{8} − 4 8 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

4 9 − 6 3 4\sqrt{9}-6\sqrt{3} 4 9 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 6 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

5 12 5\sqrt{12} 5 1 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Surds

Authored by Donald Ndombi

Mathematics

11th - 12th Grade

CCSS covered

Used 115+ times

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20 questions

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MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Simplify fully:
2√45 - 5√45 + 9√16

-9√5 + 36

-3√45 + 144

6√16

6√106

Tags

CCSS.HSN.RN.A.2

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Simplify fully:
√216

2√108

4√54

6√6

18√6

Tags

CCSS.HSN.RN.A.2

CCSS.HSN.RN.A.1

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Simplify fully:
√32

4√8

16√2

4√2

4√4

Tags

CCSS.HSN.RN.A.2

CCSS.HSN.RN.A.1

CCSS.HSA.SSE.A.2

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Simplify fully:
√120

4√30

2√30

12√10

6√10

Tags

CCSS.HSN.RN.A.2

CCSS.HSN.RN.A.1

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Simplify fully:
√32 + √12

4√2 +2√3

6√5

√44

2√11

Tags

CCSS.HSN.RN.A.2

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Rationalise the Denominator:
³/_√5

³^√5/₅

³^√5/₂₅

^√5/₅

^√5/3

Tags

CCSS.HSN.RN.A.2

CCSS.HSN.RN.A.1

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is a surd?

A recurring decimal

An irrational number

A fraction

A rational number

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Surds

Simplify fully:
2√45 - 5√45 + 9√16

Simplify fully:
√216

Simplify fully:
√32

Simplify fully:
√120

Simplify fully:
√32 + √12

Rationalise the Denominator:
³/_√5

What is a surd?

Select a surd.

5√2 x 2√3

Expand and simplify.....

√5(1 - √3)

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Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Surds

Simplify fully: 2√45 - 5√45 + 9√16

Simplify fully: √216

Simplify fully: √32

Simplify fully: √120

Simplify fully: √32 + √12

Rationalise the Denominator:3/√5

What is a surd?

Select a surd.

5√2 x 2√3

Expand and simplify.....√5(1 - √3)

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Simplify fully:
2√45 - 5√45 + 9√16

Simplify fully:
√216

Simplify fully:
√32

Simplify fully:
√120

Simplify fully:
√32 + √12

Rationalise the Denominator:
³/_√5

Expand and simplify.....

√5(1 - √3)