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Operations with Radicals — Easy Worksheet 1
Grade 9 · Whoobee Name: ____________________ Date: __________
Simplify. Write each answer in simplest radical form, like 5√3.
How to solve
Simplify each radical first (√12 = 2√3). Add or subtract only like radicals, the way you combine like terms: 2√3 + 5√3 = 7√3. To multiply, multiply the numbers outside and the numbers inside: 2√3 · 4√5 = 8√15, then simplify. To rationalize, multiply the top and bottom by the radical in the denominator.
Example
3√6 + 9√6
Answer: 12√6
Not quite. The answer is
💡 Both terms have √3, so they are like radicals. Combine the numbers in front, the way you combine like terms: 8 + 7 = 15. The answer is 15√3.
✓ Correct!
Not quite. The answer is
💡 Both terms have √3, so they are like radicals. Combine the numbers in front, the way you combine like terms: 8 + 7 = 15. The answer is 15√3.
💡 How to solve: Operations with Radicals
Simplify each radical first (√12 = 2√3). Add or subtract only like radicals, the way you combine like terms: 2√3 + 5√3 = 7√3. To multiply, multiply the numbers outside and the numbers inside: 2√3 · 4√5 = 8√15, then simplify. To rationalize, multiply the top and bottom by the radical in the denominator.
Try a similar one
2√2 + 8√2
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Multiply the numbers under the roots: √7 · √3 = √21. 21 has no perfect-square factor except 1, so √21 is already simplified. The answer is √21.
✓ Correct!
Not quite. The answer is
💡 Multiply the numbers under the roots: √7 · √3 = √21. 21 has no perfect-square factor except 1, so √21 is already simplified. The answer is √21.
💡 How to solve: Operations with Radicals
Simplify each radical first (√12 = 2√3). Add or subtract only like radicals, the way you combine like terms: 2√3 + 5√3 = 7√3. To multiply, multiply the numbers outside and the numbers inside: 2√3 · 4√5 = 8√15, then simplify. To rationalize, multiply the top and bottom by the radical in the denominator.
Try a similar one
7√11 + 3√11
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Both terms have √3, so they are like radicals. Combine the numbers in front, the way you combine like terms: 2 + 8 = 10. The answer is 10√3.
✓ Correct!
Not quite. The answer is
💡 Both terms have √3, so they are like radicals. Combine the numbers in front, the way you combine like terms: 2 + 8 = 10. The answer is 10√3.
💡 How to solve: Operations with Radicals
Simplify each radical first (√12 = 2√3). Add or subtract only like radicals, the way you combine like terms: 2√3 + 5√3 = 7√3. To multiply, multiply the numbers outside and the numbers inside: 2√3 · 4√5 = 8√15, then simplify. To rationalize, multiply the top and bottom by the radical in the denominator.
Try a similar one
5√6 + √6
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Multiply the numbers under the roots: √11 · √10 = √110. 110 has no perfect-square factor except 1, so √110 is already simplified. The answer is √110.
✓ Correct!
Not quite. The answer is
💡 Multiply the numbers under the roots: √11 · √10 = √110. 110 has no perfect-square factor except 1, so √110 is already simplified. The answer is √110.
💡 How to solve: Operations with Radicals
Simplify each radical first (√12 = 2√3). Add or subtract only like radicals, the way you combine like terms: 2√3 + 5√3 = 7√3. To multiply, multiply the numbers outside and the numbers inside: 2√3 · 4√5 = 8√15, then simplify. To rationalize, multiply the top and bottom by the radical in the denominator.
Try a similar one
3√10 + 5√10
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Both terms have √10, so they are like radicals. Combine the numbers in front, the way you combine like terms: 9 + 6 = 15. The answer is 15√10.
✓ Correct!
Not quite. The answer is
💡 Both terms have √10, so they are like radicals. Combine the numbers in front, the way you combine like terms: 9 + 6 = 15. The answer is 15√10.
💡 How to solve: Operations with Radicals
Simplify each radical first (√12 = 2√3). Add or subtract only like radicals, the way you combine like terms: 2√3 + 5√3 = 7√3. To multiply, multiply the numbers outside and the numbers inside: 2√3 · 4√5 = 8√15, then simplify. To rationalize, multiply the top and bottom by the radical in the denominator.
Try a similar one
6√3 + 9√3
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Multiply the numbers under the roots: √5 · √3 = √15. 15 has no perfect-square factor except 1, so √15 is already simplified. The answer is √15.
✓ Correct!
Not quite. The answer is
💡 Multiply the numbers under the roots: √5 · √3 = √15. 15 has no perfect-square factor except 1, so √15 is already simplified. The answer is √15.
💡 How to solve: Operations with Radicals
Simplify each radical first (√12 = 2√3). Add or subtract only like radicals, the way you combine like terms: 2√3 + 5√3 = 7√3. To multiply, multiply the numbers outside and the numbers inside: 2√3 · 4√5 = 8√15, then simplify. To rationalize, multiply the top and bottom by the radical in the denominator.
Try a similar one
9√10 + 2√10
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Both terms have √10, so they are like radicals. Combine the numbers in front, the way you combine like terms: 2 + 1 = 3. The answer is 3√10.
✓ Correct!
Not quite. The answer is
💡 Both terms have √10, so they are like radicals. Combine the numbers in front, the way you combine like terms: 2 + 1 = 3. The answer is 3√10.
💡 How to solve: Operations with Radicals
Simplify each radical first (√12 = 2√3). Add or subtract only like radicals, the way you combine like terms: 2√3 + 5√3 = 7√3. To multiply, multiply the numbers outside and the numbers inside: 2√3 · 4√5 = 8√15, then simplify. To rationalize, multiply the top and bottom by the radical in the denominator.
Try a similar one
3√10 + √10
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Multiply the numbers under the roots: √5 · √10 = √50. Largest perfect-square factor: 50 = 25 × 2, so √50 = √25 × √2 = 5√2. The answer is 5√2.
✓ Correct!
Not quite. The answer is
💡 Multiply the numbers under the roots: √5 · √10 = √50. Largest perfect-square factor: 50 = 25 × 2, so √50 = √25 × √2 = 5√2. The answer is 5√2.
💡 How to solve: Operations with Radicals
Simplify each radical first (√12 = 2√3). Add or subtract only like radicals, the way you combine like terms: 2√3 + 5√3 = 7√3. To multiply, multiply the numbers outside and the numbers inside: 2√3 · 4√5 = 8√15, then simplify. To rationalize, multiply the top and bottom by the radical in the denominator.
Try a similar one
3√11 + 6√11
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Operations with Radicals — Easy Worksheet 1
Simplify. Write each answer in simplest radical form, like 5√3.