Rational & Irrational Numbers Practice Set 1.4

Explanation :

Actually such numbers are not rational numbers they are irrational numbers.

1. First Draw a number line and place a point ‘A’ at number 1.
2. Draw perpendicular line at point A.
3. Set the point ‘F’ on perpendicular line at distance ‘0 to 1’. It means 𝒍(OA) = 𝒍(AF)
4. Draw Then joined the segment OF.
5. With this ∆OAF will be formed.
⎳A = 90⁰, 𝒍(OA) = 𝒍(AF) = 1 (unit)
By Pythagoras theorem,
𝒍(OF)² = 𝒍(OA)² + 𝒍(AF)²
𝒍(OF)² = 1² + 1²
𝒍(OF)² = 1 + 1
𝒍(OF)² = 2
𝒍(OF) = √2…(..taken square root of both sides)


6. Now draw an arc from the point ‘O’ and radius OF.
7. Observe the intersect point ‘Q’ on the line.
∴ 𝒍(OF) = 𝒍(OQ) = √2 unit.

Practice Set 1.4

(1) The number √2 is shown on a number line. Steps are given to show √2 on the number line using √2. Fill in the boxes properly and complete the activity.

Ans : The point Q on the number line shows the number √2.

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(3*) Show the number √7 on the number line.

Explanation for √5
by Pythagoras theorem,
𝒍(OP)² = 𝒍(OA)² + 𝒍(AP)²
𝒍(OP)² = 2² + 1²
𝒍(OP)² = 4 + 1
𝒍(OP)² = 5
𝒍(OP) = √5…(..taken square root of both sides)

∴ 𝒍(OP) = 𝒍(OB) = √5 unit.

Explanation for √7
by Pythagoras theorem,
𝒍(OR)² = 𝒍(OC)² + 𝒍(CR)²
𝒍(OR)² = √6² + 1²
𝒍(OR)² = 6 + 1
𝒍(OR)² = 7
𝒍(OR) = √7 …(..taken square root of both sides)

∴ 𝒍(OR) = 𝒍(OD) = √7 unit.

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Examples for practice :

Lesson No.1

➦ Practice Set 1.1
➥ Practice Set 1.2
➦ Practice Set 1.3

इतर लिंक्स :
➥ मराठी रंग :
➦ विशेषण व विशेषणाचे प्रकार
➥ सर्वनामाचे प्रकार