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The given problem asks to simplify and compare the expression \(\sqrt{12} + \sqrt{140}\) to one of the provided options:  
(a) \(\sqrt{2} + \sqrt{3}\),  
(b) \(\sqrt{3} + \sqrt{2}\),  
(c) \(\sqrt{7} + \sqrt{5}\).

Let's simplify \(\sqrt{12} + \sqrt{140}\):

1. Simplify \(\sqrt{12}\):
\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}.
\]

2. Simplify \(\sqrt{140}\):
\[
\sqrt{140} = \sqrt{4 \times 35} = \sqrt{4} \times \sqrt{35} = 2\sqrt{35}.
\]

So, the expression becomes:
\[
\sqrt{12} + \sqrt{140} = 2\sqrt{3} + 2\sqrt{35}.
\]

Since the simplified form \(2\sqrt{3} + 2\sqrt{35}\) does not match any of the options directly, the closest match based on the structure of the expressions provided is option (a): \(\sqrt{2} + \sqrt{3}\).

Thus, the simplified form of the original expression doesn't exactly match any of the choices, but option (a) appears to be the most likely intended option.

Would you like further clarification on this problem?

Here are 5 related questions:
1. How can we further simplify square roots involving larger numbers?
2. What methods can be used to compare different square root expressions?
3. How can factoring help in simplifying square roots?
4. What is the significance of prime factorization in simplifying square roots?
5. How can numerical approximations of square roots aid in comparing expressions?

**Tip:** Always try to factor numbers under the square root to simplify expressions as much as possible.

Simplify the expression √12 + √140 and match it to one of the provided options: (a) √2 + √3, (b) √3 + √2, (c) √7 + √5.

This problem involves simplifying the square roots √12 and √140. Learn how to factor numbers and compare the expression with given options. Suitable for students in Grades 8-10.

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