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Question

# Which of the following irrational numbers is represented by CE on the given number line?

A
7.4
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B
8.41
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C
8.4+1
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D
8.4
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Solution

## The correct option is B √8.4−1Given: AB = 8.4 units and BC = 1 unit ∴ AC = AB + BC = 9.4 units ∴ OA = OC = 4.7 units (radius of semicircle) ⇒ OB = OC – BC = 4.7 – 1 = 3.7 units Let CE be x units. Now, BD = BE = BC + CE = (1 + x) units By Pythagoras Theorem in ∆OBD: OD2=OB2+BD2 ⇒(4.7)2=(3.7)2+(1+x)2 (∵OD=OA=OC=4.7units) ⇒(1+x)2=(4.7)2−(3.7)2=(4.7−3.7)(4.7+3.7) ⇒(1+x)2=1×8.4=8.4 ⇒1+x=√8.4 ⇒x=(√8.4−1)units Therefore, CE represents (√8.4−1) units. Hence, the correct answer is option (b).

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