Question

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

• A. $\sqrt{7.4}$
• B. $\sqrt{8.4}-1$
• C. $\sqrt{8.4}+1$
• D. $\sqrt{8.4}$

Answer 1

The correct option is B $\sqrt{8.4}-1$

Given: 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:
$O{D}^2=O{B}^2+B{D}^2$
$\Rightarrow (4.7{)}^2=(3.7{)}^2+(1+x{)}^2$ $(\because OD=OA=OC=4.7units)$
$\Rightarrow (1+x{)}^2=(4.7{)}^2-(3.7{)}^2=(4.7-3.7\left)\right(4.7+3.7)$
$\Rightarrow (1+x{)}^2=1\times 8.4=8.4$
$\Rightarrow 1+x=\sqrt{8.4}$
$\Rightarrow x=(\sqrt{8.4}-1)units$
Therefore, CE represents $(\sqrt{8.4}-1)$ units.
Hence, the correct answer is option (b).