Let’s solve each problem one by one. All of these involve multiplying square roots. Remember this rule:
> √a × √b = √(a × b)
> Also, √a × √a = a (because the square root and square cancel out)
Also, if there’s a number in front (like 2√3), treat it like a coefficient:
> 2√3 × 4√5 = (2×4) × (√3×√5) = 8√15
And if you have a negative sign, just carry it through.
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Problem 1: √5 · √5
√5 × √5 = √(5×5) = √25 = 5
✔ Final:
5
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Problem 2: √10 · √2
√10 × √2 = √(10×2) = √20
Simplify √20: √(4×5) = √4 × √5 = 2√5
✔ Final:
2√5
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Problem 3: √8 · √8
√8 × √8 = √(8×8) = √64 = 8
✔ Final:
8
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Problem 4: √20 · √10
√20 × √10 = √(20×10) = √200
Simplify √200: √(100×2) = √100 × √2 = 10√2
✔ Final:
10√2
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Problem 5: √3 · √3
√3 × √3 = √9 = 3
✔ Final:
3
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Problem 6: √5 · √12
√5 × √12 = √(5×12) = √60
Simplify √60: √(4×15) = √4 × √15 = 2√15
✔ Final:
2√15
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Problem 7: 2√2 · √12
First, multiply coefficients: 2 × 1 = 2
Then multiply radicals: √2 × √12 = √24
So total: 2 × √24
Now simplify √24: √(4×6) = 2√6
So: 2 × 2√6 = 4√6
✔ Final:
4√6
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Problem 8: √5 · 2√2
Coefficients: 1 × 2 = 2
Radicals: √5 × √2 = √10
So: 2√10
✔ Final:
2√10
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Problem 9: √6 · (-2√6)
Coefficients: 1 × (-2) = -2
Radicals: √6 × √6 = √36 = 6
So: -2 × 6 = -12
✔ Final:
-12
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Problem 10: √2 · (-2√5)
Coefficients: 1 × (-2) = -2
Radicals: √2 × √5 = √10
So: -2√10
✔ Final:
-2√10
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Problem 11: √6 · (-√9)
First, √9 = 3, so this becomes: √6 × (-3) = -3√6
✔ Final:
-3√6
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Problem 12: √5 · (-5√5)
Coefficients: 1 × (-5) = -5
Radicals: √5 × √5 = √25 = 5
So: -5 × 5 = -25
✔ Final:
-25
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Final Answer:
1) 5
2) 2√5
3) 8
4) 10√2
5) 3
6) 2√15
7) 4√6
8) 2√10
9) -12
10) -2√10
11) -3√6
12) -25
Parent Tip: Review the logic above to help your child master the concept of multiplying square roots worksheet.
