Mastering Operations with Radicals Explained

Dhriti

11/30/2025

Algebra 1

Operations with Radicals

Subjects

Algebra 1

Exponents & Radicals

Radicals

•

Nov 30, 2025

•

2 pages

Mastering Operations with Radicals Explained

Dhriti

@dhriti_

Operations with radicals are just like working with regular numbers,... Show more

# 10.3: Operations w/ Radicals

Adding + Subtracting

*U CAN ONIY ADD/SUB "Like Radicals"

ex) $3x²+4x²=7x2$

ex.2) $5x³-2x²$= (not like ter

Adding and Subtracting Radicals

Just like you can only add 3x + 4x but not 3x + 4y, you can only add or subtract like radicals - those with the same number inside the radical sign. For example, √2 + √2 works, but √2 + √3 stays separate.

When adding like radicals, just add the numbers in front. So 5√2 + 6√2 = 11√2, and 9√3 + 8√5 - 2√3 = 7√3 + 8√5. The radical parts stay exactly the same!

Sometimes you'll need to simplify radicals first to see if they're actually alike. For example, with 4√12 - 6√48, you should break down each radical: 4√12 = 4(2√3) = 8√3 and 6√48 = 6(4√3) = 24√3. Now you can add them: 8√3 - 24√3 = -16√3.

Pro Tip: When working with complicated radical expressions, always simplify each radical first. Look for perfect squares like √4 = 2, √9 = 3, and √16 = 4 that can be pulled out of the radical.

Multiplying Radicals

Multiplying radicals is where things get interesting! You can use the distributive property just like with regular algebra. For example, when multiplying 3√5(2√5 + 5√3), distribute the 3√5 to each term inside the parentheses.

When multiplying the same radicals, like √5 · √5, the result equals √25, which simplifies to 5. This makes sense because √5 · √5 = 5.

For more complex multiplications, you have options. You can either multiply everything and then simplify, or simplify first and then multiply. The second approach is usually easier. For instance, with 4√6(5√3 + 2√4), notice that √4 = 2, so this becomes 4√6(5√3 + 4).

When using FOIL to multiply radical expressions, follow the same steps as with binomials, but be careful with the radical multiplications. Keep track of which radicals combine and which stay separate.

Remember: When multiplying radicals, √a · √b = √(a·b). This means √2 · √3 = √6, which makes multiplying different radicals much easier!

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Subjects

Algebra 1

Exponents & Radicals

Radicals

Algebra 1

•

Nov 30, 2025

•

2 pages

Mastering Operations with Radicals Explained

Dhriti

@dhriti_

Operations with radicals are just like working with regular numbers, but with special rules for the radical signs. This topic helps you understand how to add, subtract, and multiply expressions containing square roots.

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Adding and Subtracting Radicals

When adding like radicals, just add the numbers in front. So 5√2 + 6√2 = 11√2, and 9√3 + 8√5 - 2√3 = 7√3 + 8√5. The radical parts stay exactly the same!

Pro Tip: When working with complicated radical expressions, always simplify each radical first. Look for perfect squares like √4 = 2, √9 = 3, and √16 = 4 that can be pulled out of the radical.

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Access to all documents

Improve your grades

Join milions of students

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Multiplying Radicals

When multiplying the same radicals, like √5 · √5, the result equals √25, which simplifies to 5. This makes sense because √5 · √5 = 5.

Remember: When multiplying radicals, √a · √b = √(a·b). This means √2 · √3 = √6, which makes multiplying different radicals much easier!