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?​

1 answer

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.