Practice Set 1.4 8th Std Maths Answers Chapter 1 Rational and Irrational Numbers
Question 1
Maharashtra Board Solution
The number √2 is shown on a number line. Steps are given to show √3 on the number line using √2. Fill in the boxes properly and complete the activity. The point Q on the number line shows the number ………. 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 & Step-by-Step Answer:
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 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.
Question 2
Maharashtra Board Solution
Show the number √5 on the number line.
Solution & Step-by-Step Answer:
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.
Question 3
Maharashtra Board Solution
Show the number √7 on the number line.
Solution & Step-by-Step Answer:
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.