Question

Find the sum of square root of, 25, end square root 25 ​ and 4, square root of, 2, end square root4 2 ​ in simplest form.

Answer 1

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Answer 2

The result is rational because it CANNOT be written as the ratio of two integers and its decimal expansion does terminate or repeat. correct?

Answer 3

To find the sum of \( \sqrt{25} \) and \( 4\sqrt{2} \):

1. Calculate \( \sqrt{25} \):
\[
\sqrt{25} = 5
\]

2. The expression then becomes:
\[
5 + 4\sqrt{2}
\]

3. Since \( 4\sqrt{2} \) cannot be simplified further, we keep it as is.

Thus, the sum in simplest form is:
\[
\boxed{5 + 4\sqrt{2}}
\]

Answer 4

The sum of the square root of 25 and 4 times the square root of 2 can be calculated as follows:

1. The square root of 25 is 5.
2. Therefore, you have 5 plus 4 times the square root of 2.

So, the final answer is:

5 + 4√2

Answer 5

The statement you provided is not correct when referring to the expression \( 5 + 4\sqrt{2} \).

1. **Rational vs. Irrational**: A number is rational if it can be expressed as the ratio of two integers (a fraction) and its decimal representation either terminates or repeats. A number is irrational if it cannot be expressed as such a ratio.

2. **Breaking down \( 5 + 4\sqrt{2} \)**:
- The number \( 5 \) is rational.
- The number \( \sqrt{2} \) is irrational (it cannot be expressed as a fraction of two integers).
- Therefore, \( 4\sqrt{2} \) is also irrational (since multiplying an irrational number by a non-zero rational number results in an irrational number).

3. **Adding a rational and an irrational number**: When you add a rational number (5) to an irrational number (4√2), the result \( 5 + 4\sqrt{2} \) remains irrational.

In conclusion, \( 5 + 4\sqrt{2} \) is irrational, and it cannot be expressed as a ratio of two integers. Its decimal expansion does not terminate or repeat.