Question

What is the exact value for the expression the square root of 56. − the square root of 14. + the square root of 126.? Simplify if possible. (5 points)

Option 1: the square root of 14.
Option 2: 4 the square root of 14.
Option 3: 2 the square root of 42.
Option 4: 8 the square root of 42.

Answer 1

To find the exact value for the expression √56 - √14 + √126, we simplify by factoring out square roots and combining them, which results in the expression 4√14, corresponding to Option 2.

Step-by-step explanation:

The student is asking for the simplified exact value for the expression √56 - √14 + √126. To simplify this expression, we can factor out the square roots by looking for perfect squares or common factors within the radicands (the numbers inside the square root).

• √56 can be factored into √(4×14), which simplifies to 2√14.
• √14 remains the same since it cannot be factored into a smaller square root.
• √126 can be factored into √(9×14), which simplifies to 3√14.

Now we can combine these simplified terms:

2√14 - √14 + 3√14 = (2 - 1 + 3)√14 = 4√14

Therefore, the correct answer is Option 2: 4√14.