Consider the following expressions:
−34+6⋅216−−√_____4(2+6)÷2−6.
Which operator (>, <, or =) should be inserted into the blank space to make the statement true?
The expression can be simplified as follows:
-34 + 6 * 216 - √(4(2 + 6)) ÷ 2 - 6
-34 + 6 * 216 - √(4 * 8) ÷ 2 - 6
-34 + 6 * 216 - √32 ÷ 2 - 6
-34 + 1296 - 5.657 ÷ 2 - 6
Now let's solve the expression:
-34 + 1296 = 1262
-5.657 ÷ 2 ≈ -2.8285
1262 - 2.8285 - 6 = 1253.1715
To compare 1253.1715 with 1253.17, we can see that 1253.1715 is slightly greater than 1253.17.
Therefore, the operator ">" (greater than) should be inserted into the blank space to make the statement true: −34 + 6⋅216 - √(4(2 + 6)) ÷ 2 - 6 > 1253.17.
To determine which operator should be inserted into the blank space, let's simplify the expression:
−34 + 6⋅216 − −√_____4(2 + 6) ÷ 2 − 6
First, let's solve inside the parentheses:
−34 + 6⋅216 − −√_____4(8) ÷ 2 − 6
Now calculate the values inside the parentheses:
−34 + 6⋅216 − −√_____32 ÷ 2 − 6
Next, perform the multiplication and division:
−34 + 1296 − −√_____16 − 6
Now simplify the square root:
−34 + 1296 − 4_____16 − 6
Simplify further:
−34 + 1296 − 4_____10
Now evaluate the subtraction:
(−34 + 1296 − 4)_____10
Simplify the addition and division:
1258_____10
Finally, simplify the division:
125.8
So, the expression simplifies to 125.8.
But since we have a blank space in the original expression, we need to determine if it should be greater than (>), less than (<), or equal to (=) 125.8.
To answer this, we need more information about what value or expression is being compared to 125.8.