Question : Directions: Select the correct combination of mathematical signs to replace the * signs and to balance the given equation.
($\sqrt{729 * 9}$) * 67 * 81 * (4 * 6) * 19

Option 1: +, –, +, ÷, =, ×

Option 2: ×, +, –, +, ×, =

Option 3: +, –, ÷, =, –, ×

Option 4: ÷, +, =, –, ×, +

Correct Answer: ÷, +, =, –, ×, +

Solution : Given:
($\sqrt{729 * 9}$) * 67 * 81 * (4 * 6) * 19

Let's check the given options –
First option: +, –, +, ÷, =, ×
⇒ ($\sqrt{729 + 9}$) – 67 + 81 ÷ 4 = 6 × 19
Solving the L.H.S. of the equation –
= ($\sqrt{738}$) – 67 + 81 ÷ 4
= 27.1 – 67 + 81 ÷ 4
= 27.1 – 67 + 20.25
= –19.65
Solving the R.H.S. of the equation –
= 6 × 19 = 114
L.H.S. ≠ R.H.S.
Second option: ×, +, –, +, ×, =
⇒ ($\sqrt{729 × 9}$) + 67 – 81 + (4 × 6) = 19
Solving the L.H.S. of the equation –
= ($\sqrt{6561}$) + 67 – 81 + 24
= 81 + 67 – 81 + 24
= 91
L.H.S. ≠ R.H.S.
Third option: +, –, ÷, =, –, ×
⇒ ($\sqrt{729 + 9}$) – 67 ÷ 81 = (4 – 6) × 19
Solving the L.H.S. of the equation –
= ($\sqrt{738}$) – 67 ÷ 81
= 27.1 – 67 ÷ 81
= 27.1 – 0.83
= 26.27
Solving the R.H.S. of the equation –
= –2 × 19 = –38
L.H.S. ≠ R.H.S.
Fourth option: ÷, +, =, –, ×, +
⇒ ($\sqrt{729 ÷ 9}$) + 67 = 81 – (4 × 6) + 19
Solving the L.H.S. of the equation –
= ($\sqrt{81}$) + 67
= 9 + 67
= 76
Solving the R.H.S. of the equation –
= 81 – 24 + 19 = 76
L.H.S. = R.H.S.

So, only the fourth option satisfies the given equation. Hence, the fourth option is correct.