Let’s solve each problem step by step.
We’re simplifying expressions with radicals (square roots). The key idea:
→ You can only add or subtract radicals if they have the
same number under the root (like terms).
→ If they don’t match, simplify the radical first (break it into a whole number times a simpler radical), then combine like terms.
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Problem 1:
3√6 – 4√6
Both terms have √6 → combine coefficients: 3 – 4 = -1
→ Answer:
-√6
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Problem 2:
-3√7 + 4√7
Both have √7 → -3 + 4 = 1
→ Answer:
√7
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Problem 3:
-11√21 – 11√21
Same radical → -11 – 11 = -22
→ Answer:
-22√21
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Problem 4:
-9√15 + 10√15
Same radical → -9 + 10 = 1
→ Answer:
√15
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Problem 5:
-10√7 + 12√7
Same radical → -10 + 12 = 2
→ Answer:
2√7
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Problem 6:
-3√17 – 4√17
Same radical → -3 – 4 = -7
→ Answer:
-7√17
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Problem 7:
-10√11 – 11√11
Same radical → -10 – 11 = -21
→ Answer:
-21√11
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Problem 8:
-2√3 + 3√27
First, simplify √27.
27 = 9 × 3 → √27 = √(9×3) = √9 × √3 = 3√3
So now: -2√3 + 3×(3√3) = -2√3 + 9√3
Now combine: -2 + 9 = 7
→ Answer:
7√3
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Problem 9:
2√6 – 2√24
Simplify √24: 24 = 4×6 → √24 = √(4×6) = 2√6
So: 2√6 – 2×(2√6) = 2√6 – 4√6
Combine: 2 – 4 = -2
→ Answer:
-2√6
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Problem 10:
2√6 + 3√54
Simplify √54: 54 = 9×6 → √54 = √(9×6) = 3√6
So: 2√6 + 3×(3√6) = 2√6 + 9√6
Combine: 2 + 9 = 11
→ Answer:
11√6
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Problem 11:
-√12 + 3√3
Simplify √12: 12 = 4×3 → √12 = √(4×3) = 2√3
So: -2√3 + 3√3
Combine: -2 + 3 = 1
→ Answer:
√3
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Problem 12:
3√3 – √27
Simplify √27: 27 = 9×3 → √27 = 3√3
So: 3√3 – 3√3 = 0
→ Answer:
0
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Final Answer:
1) -√6
2) √7
3) -22√21
4) √15
5) 2√7
6) -7√17
7) -21√11
8) 7√3
9) -2√6
10) 11√6
11) √3
12) 0
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting radical expressions worksheet answers.
