Solve (square root2 + square root 5) + (square root 2-square root 5

Let's solve the expression step by step:

\[
(\sqrt{2} + \sqrt{5}) + (\sqrt{2} - \sqrt{5})
\]

### Step 1: Group the like terms
We can combine the terms with \(\sqrt{2}\) and the terms with \(\sqrt{5}\):

\[
(\sqrt{2} + \sqrt{2}) + (\sqrt{5} - \sqrt{5})
\]

### Step 2: Simplify
- \(\sqrt{2} + \sqrt{2} = 2\sqrt{2}\)
- \(\sqrt{5} - \sqrt{5} = 0\)

Thus, the expression becomes:

\[
2\sqrt{2} + 0 = 2\sqrt{2}
\]

### Final Answer:
\[
2\sqrt{2}
\]

Would you like further explanation or assistance with another problem? Here are some related questions:

1. What happens if you subtract the two terms instead of adding them?
2. How do you simplify expressions with square roots of numbers that can't be simplified further?
3. Can you express \(2\sqrt{2}\) as a decimal approximation?
4. What is the result if you multiply \(\sqrt{2}\) and \(\sqrt{5}\)?
5. How do you handle sums or differences of square roots in other algebraic expressions?

**Tip:** When adding or subtracting square roots, only like terms can be combined—just as with regular variables like \(x\) or \(y\).

Solve (square root 2 + square root 5) + (square root 2 - square root 5)

Learn how to simplify the expression (√2 + √5) + (√2 - √5) step by step. This problem covers simplifying square roots and combining like terms. Suitable for students in Grades 7-9.

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