Simplification Test - 8

Expression:

( 47.932 + 56 + 97.168 - 67 - 78.3 - 22.7 )

Step 1: Add the positive terms:

( 47.932 + 56 + 97.168 = 201.1 )

Step 2: Add the negative terms:

( 67 + 78.3 + 22.7 = 168 )

Step 3: Subtract the sum of negative terms from the sum of positive terms:

( 201.1 - 168 = 33.1 )

Final Answer: The result of the expression is  33.1 .

• To solve 4789300 x 11, we can break it down.
• First, multiply 4789300 by 10, which gives 47893000.
• Next, add 4789300 to that result (because 11 is 10 + 1).
• So, 47893000 + 4789300 = 52682300.
• The correct answer is 52682300, which is option 1.

To solve the expression:

6 1/4 + 0.25 + 0.75 - 0.3125 = ?

Step 1: Convert the mixed fraction to a decimal.

6  ¹ ⁄₄     = 6.25)

Now, substitute (6.25) into the expression:

Expression: (6.25 + 0.25 + 0.75 - 0.3125)

Step 2: Calculate each operation:

• (6.25 + 0.25 = 6.5)
• (6.5 + 0.75 = 7.25)
• (7.25 - 0.3125 = 6.9375)

Answer: a) 6.9375

∛(-1728 ×-2197)

1728 can be written as 12 ×12 ×12
2197 can be written as 13 ×13 ×13

So,

∛(-1728 ×-2197)
= ∛(-12 ×-12 ×-12) ×∛(-13 ×-13 ×-13)
= ∛((-12)³) ×∛((-13)³)
= (-12 ³)^1/3 ×(-13 ³)^1/3

= -12 x - 13

= 156

∴∛(-1728 ×-2197) = 156

To solve the problem, follow these steps:

• First, handle the whole numbers:
  • 4 - 3 equals 1 .
  • 13 - 8 equals 5 .
• Next, calculate the fractions:
  • Convert 1/2 and 1/7 to a common denominator:
    • 1/2 becomes 7/14 .
    • 1/7 becomes 2/14 .
  • Subtract to get 5/14 .
  • Convert 2/7 and 1/4 to a common denominator:
    • 2/7 becomes 8/28 .
    • 1/4 becomes 7/28 .
  • Subtract to get 1/28 .
• Add the fractions 5/14 and 1/28 :
  • Convert 5/14 to 10/28 .
  • Add to get 11/28 .
• Combine the whole number and the fraction:
  • The result is 6 11/28 .

= we know,
(4-3+13-8)+(1/2 - 1/7 + 2/7 -1/4)
= 6 + 11/28
6 11/28
= option C  

Given equation:
√169 ×256 = (?)²×13
Step 1: Calculate the square root of 169
√169 = 13
Substitute this value back into the equation:
13 ×256 = (?)²×13

Step 2: Divide both sides by 13
256 = (?)²

Step 3: Solve for ( ? )
Taking the square root of both sides:
? = √256 = 16

The answer is: d) 16

The correct option is C.
(7x?)² /49 = √81
⇒(49x?)/49= √81
⇒x² = √81
⇒x² = 9
⇒x = 3

Given expression
10 1/2 - [8 1/2 + {6 - (7 - 6 - 4)}]
21/2 -[17/2+ { 6 - (7-10)]
21/2 - [17/2 + (6+3)]
21/2 - 17/2 - 9
2 - 9 = -7
 

Given,

14.998% of 619.999 =?

It can also be approximated as

= 15% of 600
= (15 x 600)/100
= 90

Given,

2³  ×3⁴  ×1080 ÷15 = 6^x

⇒2³  ×3⁴  ×72 = 6^x

⇒2³  ×3⁴  ×(2 ×6² ) = 6^x

⇒2⁴  ×3⁴  ×6²  = 6^x

⇒(2 ×3)⁴  ×6²  = 6^x           [∵x^m  ×y^m  = (xy)^m ]

⇒6⁴  ×6²  = 6^x

⇒6^{(4 + 2)}  = 6^x

⇒x = 6

x = √(380 + √(380 + √(380 + √(380 + ... ∞))))
x²   = 380 + x
x²   -x - 380 = 0
(x - 20)(x + 19)