Add 28–√+28−−√+28–√



HINT: What is alike in this problem? Combine that and then you will have an equation of what is left.

(1 point)
Responses

416−−√+28−−√
4 square root of 16 plus square root of 28

48–√+28−−√
4 square root of 8 plus square root of 28

544−−√

1 answer

To add the expressions \( \sqrt{28} + \sqrt{28} + \sqrt{28} \), we can start by simplifying the square root of 28.

The square root of 28 can be simplified as follows: \[ \sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \cdot \sqrt{7} = 2\sqrt{7} \]

Now we can combine the three \( \sqrt{28} \) terms: \[ \sqrt{28} + \sqrt{28} + \sqrt{28} = 3\sqrt{28} = 3 \cdot 2\sqrt{7} = 6\sqrt{7} \]

Given the options and simplifying further does not seem necessary, \( 6\sqrt{7} \) is the simplification of the expression. However, none of the provided answers directly match this expression.

It's important to verify the choices:

  1. \( 4\sqrt{16} + \sqrt{28} \) simplifies to \( 16 + \sqrt{28} \) which is incorrect.
  2. \( 4\sqrt{8} + \sqrt{28} \) simplifies to \( 4 \cdot 2\sqrt{2} + \sqrt{28} = 8\sqrt{2} + \sqrt{28} \) which also doesn't lead us to \( 6\sqrt{7} \).
  3. \( 544-\sqrt{} \) seems incomplete or incorrect as a possible sum.

Therefore, none of the options correctly represent the sum of the expression \( \sqrt{28} + \sqrt{28} + \sqrt{28} \). The correct simplification is \( 6\sqrt{7} \).