Add or subtract, as indicated. See Example 6. √6 + √7

Verified step by step guidance

1. Identify the terms involved: \( \sqrt{6} \) and \( \sqrt{7} \). Both are square roots of different numbers.
2. Recall that square roots can only be combined through addition or subtraction if they have the same radicand (the number inside the root). Here, \( \sqrt{6} \) and \( \sqrt{7} \) have different radicands.
3. Since the radicands are different, these terms are unlike radicals and cannot be simplified by addition or subtraction directly.
4. Therefore, the expression \( \sqrt{6} + \sqrt{7} \) remains as it is because it cannot be combined further.
5. If needed, you can approximate each square root separately using a calculator, but the exact simplified form is just the sum of the two square roots.

Key Concepts

Simplifying Radicals

Simplifying radicals involves expressing square roots in their simplest form by factoring out perfect squares. This helps in identifying like terms and making addition or subtraction possible. For example, √18 can be simplified to 3√2 by factoring 18 as 9×2.

Like Radicals

Like radicals have the same radicand (the number inside the square root). Only like radicals can be added or subtracted directly by combining their coefficients. For instance, 2√3 + 5√3 equals 7√3, but √6 + √7 cannot be combined since 6 and 7 differ.

Addition and Subtraction of Radicals

Adding or subtracting radicals requires first simplifying them and then combining only like radicals. If radicals are unlike, they remain separate terms in the expression. This concept is similar to combining like terms in algebra, ensuring operations are valid.