Question

If the value \(\dfrac{(1.25)^3+2.25\times(1.25)^2+(3.75)\times(0.75)^2+(0.75)^3}{(1.25)^3-2.25(1.25)^2+3\times1.25(0.75)^2-(0.75)(0.5625)}\) is x, then √x is equal to:
1. 8
2. 0.4
3. 0.8
4. 4

Answer 1

Correct Answer - Option 1 : 8

Formula used:

(a + b)³ = a³ + b³ + 3ab² + 3a²b

(a - b)3 = a3 - b3 - 3ab2 + 3a2b

Calculation:

\(\dfrac{(1.25)^3+2.25\times(1.25)^2+(3.75)\times(0.75)^2+(0.75)^3}{(1.25)^3-2.25(1.25)^2+3\times1.25(0.75)^2-(0.75)(0.5625)}\)

⇒ \(\dfrac{(1.25)^3+3 \times 0.75\times(1.25)^2+ 3 \times 0.75\times(0.75)^2+(0.75)^3}{(1.25)^3- 3 \times 0.75 \times (1.25)^2+3\times1.25 \times (0.75)^2-(0.75)^3}\)

⇒ \(\dfrac{(1.25 + 0.75)^3}{(1.25 - 0.75)^3}\)

⇒ \(\dfrac{(2)^3}{(0.50)^3}\)

⇒ \(\dfrac{8}{0.125}\)

⇒ x = 64

So, √x = √64 = 8

Hence, "8" is the correct answer.