Let's simplify each square root step by step. The goal is to
factor out perfect squares from under the square root and simplify.
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1) √40
Factor 40:
40 = 4 × 10
√40 = √(4 × 10) = √4 × √10 = 2√10
✔ Answer:
2√10
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2) √50
Factor 50:
50 = 25 × 2
√50 = √(25 × 2) = √25 × √2 = 5√2
✔ Answer:
5√2
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3) √200
Factor 200:
200 = 100 × 2
√200 = √(100 × 2) = √100 × √2 = 10√2
✔ Answer:
10√2
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4) √75
Factor 75:
75 = 25 × 3
√75 = √(25 × 3) = √25 × √3 = 5√3
✔ Answer:
5√3
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5) √18
Factor 18:
18 = 9 × 2
√18 = √(9 × 2) = √9 × √2 = 3√2
✔ Answer:
3√2
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6) √12
Factor 12:
12 = 4 × 3
√12 = √(4 × 3) = √4 × √3 = 2√3
✔ Answer:
2√3
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7) √32
Factor 32:
32 = 16 × 2
√32 = √(16 × 2) = √16 × √2 = 4√2
✔ Answer:
4√2
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8) √72
Factor 72:
72 = 36 × 2
√72 = √(36 × 2) = √36 × √2 = 6√2
✔ Answer:
6√2
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9) √45
Factor 45:
45 = 9 × 5
√45 = √(9 × 5) = √9 × √5 = 3√5
✔ Answer:
3√5
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10) √98
Factor 98:
98 = 49 × 2
√98 = √(49 × 2) = √49 × √2 = 7√2
✔ Answer:
7√2
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✔ Final Answers:
1) √40 =
2√10
2) √50 =
5√2
3) √200 =
10√2
4) √75 =
5√3
5) √18 =
3√2
6) √12 =
2√3
7) √32 =
4√2
8) √72 =
6√2
9) √45 =
3√5
10) √98 =
7√2
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🔍 Summary of Method:
To simplify a square root:
- Break the number into a product of a
perfect square and another number.
- Take the square root of the perfect square outside the radical.
- Leave the other factor inside the square root.
Example:
√50 = √(25 × 2) = √25 × √2 = 5√2
Let me know if you'd like a printable version or explanation for any specific one!
Parent Tip: Review the logic above to help your child master the concept of simplify square root worksheet.
