5. Simplify. (Image: negative 11 start root 112 end root) (1 point)
(Image: negative 44 Start Root 7 End Root)
(Image: negative 176 Start Root 7 End Root)
(Image: negative 27 Start Root 7 End Root)
(Image: 4 Start Root 7 End Root)
-2√28
-4√7
-16√7
-3√7
2√7
-44√7
-176√7
-27√7
-4√7
Sorry about that, I made a mistake in my previous response. The correct answers are:
-11√112 = -22√28 (simplified by factoring out 4 from 112, then taking the square root of 4 and simplifying the remaining square root of 28 to 2√7)
-44√7 (fully simplified)
-176√7 (fully simplified)
-27√7 (fully simplified)
4√7
5. Simplify. -11√112 (1 point)
-44√7
-176√7
-27√7
-4√7
-11√112 can be simplified as follows:
-11√112 = -11√(16 x 7) (16 is a perfect square factor of 112)
= -11 x 4√7 (square root of 16 is 4)
= -44√7
Therefore, the simplified form of -11√112 is -44√7.
So, the correct answer is option (b) -44√7.
To simplify these expressions involving square roots, you need to simplify each individual square root separately.
For the first expression (-11√112), you start by finding the perfect square factors of 112. In this case, 16 is a perfect square that can be factored out. So you can rewrite the expression as -11√(16 × 7). Taking the square root of 16 gives us 4, so the expression simplifies to -11 × 4√7 = -44√7.
For the second expression (-44√7), there are no perfect square factors in the square root. So this expression is already simplified.
For the third expression (-176√7), we can again look for perfect square factors. This time, 4 is a perfect square that can be factored out. So the expression becomes -176√(4 × 7). Taking the square root of 4 gives us 2, so the expression simplifies to -176 × 2√7 = -352√7.
For the fourth expression (-27√7), there are no perfect square factors, so it is already simplified.
Finally, for the last expression (4√7), no perfect square factors can be factored out, so this expression is also already simplified.
So, after simplifying each expression, we have:
-11√112 = -44√7
-44√7 = -44√7
-176√7 = -352√7
-27√7 = -27√7
4√7 = 4√7