**About this page:** Rational and Irrational numbers with Practice Set 1.4

**About this page:**Rational and Irrational numbers with Practice Set 1.

Here is the Rational numbers & Irrational numbers Practice set, We have solved the Practice set 1.4 . Before that we will learn about how to show square root numbers on number line.

**Practice Set 1.**4

Ans:

A line perpendicular to the number line is drawn through the point Q. Point R is at unit distance from Q on the line.

Right angled ∆OQR is obtained by drawing seg OR.

l(OQ) = √2, l(QR) = 1

∴By Pythagoras theorem,

[l(OR)]² = [l(OQ)]² + [l(QR)]²

Draw an arc with centre O and radius OR. Mark the point of intersection of the line and the arc as C. The point C shows the number √3

Solution:

The point Q on the number line shows the number √2

A line perpendicular to the number line is drawn through the point Q. Point R is at unit distance from Q on the line.

Right angled ∆OQR is obtained by drawing seg OR.

l(OQ) = √2, l(QR) = 1

∴By Pythagoras theorem,

[l(OR)]² = [l(OQ)]² + [l(QR)]²

….[Taking square root of both sides]

Draw an arc with center O and radius OR. Mark the point of intersection of the line and the arc as C. The point C shows the number √3.

Ans:

Draw a number line and take a point Q at 2

such that l(OQ) = 2 units.

Draw a line QR perpendicular to the number line through the point Q such that l(QR) = 1 unit.

Draw seg OR.

∆OQR formed is a right angled triangle.

By Pythagoras theorem,

[l(OR)]² = [l(OQ)]² + [l(QR)]²

= 2² + 1²

= 4 + 1

= 5

∴l(OR) = √5 units ….[Taking square root of both sides]

Draw an arc with center O and radius OR. Mark the point of intersection of the number line and arc as C. The point C shows the number √5.

Ans:

Draw a number line and take a point Q at 2 such that l(OQ) = 2 units.

Draw a line QR perpendicular to the number line through the point Q such that l(QR) = 1 unit.

Draw seg OR.

∆OQR formed is a right angled triangle.

By Pythagoras theorem,

[l(OR)]² = [l(OQ)]² + [l(QR)]²

= 2² + 1²

= 4 + 1

= 5

∴ l(OR) = √5 units .… [Taking square root of both sides]

Draw an arc with centre O and radius OR.

Mark the point of intersection of the number line and arc as C. The point C shows the number √5.

Similarly, draw a line CD perpendicular to the number line through the point C such that l(CD) = 1 unit.

By Pythagoras theorem,

l(OD) = √6 units

The point E shows the number √6 .

Similarly, draw a line EP perpendicular to the number line through the point E such that l(EP) = 1 unit.

By Pythagoras theorem,

l(OP) = √7 units. The point F shows the number √7.

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