Irrational Numbers Number Line

Place the number √7 between which two whole numbers on the number line.

• 2 and 3

• 3 and 4

• 1 and 2

• 4 and 5

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CCSS.8.NS.A.2

Identify the irrational number represented by Point F.

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CCSS.8.NS.A.2

Which of these irrational numbers is between 9 and 10 on the number line?

• √9.3

• 3√3

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CCSS.8.NS.A.2

Identify the irrational number represented by Point B.

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CCSS.8.NS.A.2

Determine which irrational number Point G corresponds to.

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CCSS.8.NS.A.2

Determine which irrational number Point A corresponds to.

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CCSS.8.NS.A.2

Which points are greater than √5 ?

• Point M

• Point N

• Point P

• None of the above

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CCSS.8.NS.A.2

Which is the best approximation of point P?

• √8

• √2.8

• 17/5

• 2 1/4

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CCSS.8.NS.A.2

Which value best approximates point R?

• 18/4

• √50.9

• √7.13

• π²

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CCSS.8.NS.A.2

Which of the following options is correct?

• √6.5 comes between 2 and 3 on the number line

• √6.5 comes between -2 and -3 on the number line

• √6.5 comes between 1 and 2 on the number line

• √6.5 comes between 3 and 4 on the number line

Answer explanation

To represent √6.5 on the number line, we will take a line segment AB such that AB = 6.5 cm From B, take a distance of 1 unit and mark the new point as C. Consider the point B as 0 and mark points on number line at unit distance from each other. Now we will take the midpoint of AC (AB + BC) / 2 = (6.5 + 1) / 2 = 7.5 / 2 = 3.75 From point C move towards left and take a distance of 3.75 and name that point as O. Now we will draw semicircle with centre O and radius OC = 3.75cm. Draw a perpendicular at B that intersects the semicircle at D. Join OD. Now, AB = 6.5 units AO = OC = 3.75 units OB = AB - AO = 6.5 - 3.75 = 2.75 units By pythagoras theorem BD² = OD² - OB² = (3.75)² - (2.75)² = 14.0625 - 7.5625 BD² = 6.5 BD = √6.5 Now we will draw an arc by taking BD as the radius which will intersect the number line between 2 and 3.

Tags

CCSS.8.NS.A.2