Let’s solve each problem step by step. We’re simplifying radicals — that means we combine terms that have the same square root (like √3, √2, etc.), just like combining apples with apples and oranges with oranges.
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Problem 1:
2√3 + 2√3 – 3√3
→ Add coefficients of √3: 2 + 2 = 4 → then 4 – 3 = 1
→ So,
1√3 or just
√3
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Problem 2:
7√2 + 5√2 – 6√2
→ 7 + 5 = 12 → 12 – 6 = 6
→ So,
6√2
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Problem 3:
8√17 – √17 + 6√17
→ Think of “– √17” as “–1√17”
→ 8 – 1 = 7 → 7 + 6 = 13
→ So,
13√17
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Problem 4:
11√3 – 2√11 + 5√11
→ Here, √3 and 11 are different — can’t combine them.
→ Combine only the √11 terms: –2√11 + 5√11 = 3√11
→ Leave 11√3 alone
→ So,
11√3 + 3√11
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Problem 5:
5√5 + 4√5 – 3√5
→ 5 + 4 = 9 → 9 – 3 = 6
→ So,
6√5
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Problem 6:
8√2 + 4√2 – 3√2
→ 8 + 4 = 12 → 12 – 3 = 9
→ So,
9√2
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Problem 7:
9√11 – 8√11 + √11
→ “+ √11” is same as “+1√11”
→ 9 – 8 = 1 → 1 + 1 = 2
→ So,
2√11
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Problem 8:
5√3 – 5√3 + 4√2
→ 5√3 – 5√3 = 0
→ Left with
4√2
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Problem 9:
6√5 – 2√3 + 2√5
→ Combine √5 terms: 6√5 + 2√5 = 8√5
→ –2√3 stays as is (different radical)
→ So,
8√5 – 2√3
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Final Answer:
√3
6√2
13√17
11√3 + 3√11
6√5
9√2
2√11
4√2
8√5 – 2√3
Parent Tip: Review the logic above to help your child master the concept of algebra math sheets.
