Let’s solve each problem step by step. We’re multiplying square roots, and many of them are perfect squares — that means their square roots are whole numbers.
Remember:
√a × √b = (a×b)
But if both a and b are perfect squares, it’s easier to take the square root first, then multiply.
We’ll go row by row.
---
Row 1:
√225 × √4
√225 = 15 (because 15×15=225)
√4 = 2 (because 2×2=4)
15 × 2 =
30
√9 × √625
√9 = 3
√625 = 25 (because 25×25=625)
3 × 25 =
75
---
Row 2:
√64 × √81
√64 = 8
√81 = 9
8 × 9 =
72
√16 × √144
√16 = 4
√144 = 12
4 × 12 =
48
---
Row 3:
√4 × √9
√4 = 2
√9 = 3
2 × 3 =
6
√144 × √4
√144 = 12
√4 = 2
12 × 2 =
24
---
Row 4:
√9 × √144
√9 = 3
√144 = 12
3 × 12 =
36
√36 × √144
√36 = 6
√144 = 12
6 × 12 =
72
---
Row 5:
√49 × √144
√49 = 7
√144 = 12
7 × 12 =
84
√16 × √64
√16 = 4
√64 = 8
4 × 8 =
32
---
Row 6:
√144 × √4
√144 = 12
√4 = 2
12 × 2 =
24
√100 × √16
√100 = 10
√16 = 4
10 × 4 =
40
---
Row 7:
√144 × √4
Same as above → 12 × 2 =
24
√784 × √16
√784 = 28 (because 28×28=784)
√16 = 4
28 × 4 =
112
---
Row 8:
√25 × √400
√25 = 5
√400 = 20
5 × 20 =
100
√25 × √100
√25 = 5
√100 = 10
5 × 10 =
50
---
Row 9:
√25 × √400
Same as above → 5 × 20 =
100
√225 × √4
√225 = 15
√4 = 2
15 × 2 =
30
---
Row 10:
√64 × √9
√64 = 8
√9 = 3
8 × 3 =
24
√225 × √9
√225 = 15
√9 = 3
15 × 3 =
45
---
Row 11:
√196 × √9
√196 = 14 (because 14×14=196)
√9 = 3
14 × 3 =
42
√441 × √9
√441 = 21 (because 21×21=441)
√9 = 3
21 × 3 =
63
---
Row 12:
√9 × √225
√9 = 3
√225 = 15
3 × 15 =
45
√1 × √16
√1 = 1
√16 = 4
1 × 4 =
4
---
Now let’s list all answers in order, left to right, top to bottom:
Left column:
30, 72, 6, 36, 84, 24, 24, 100, 100, 24, 42, 45
Right column:
75, 48, 24, 72, 32, 40, 112, 50, 30, 45, 63, 4
Wait — let me double-check the pairing. The worksheet has two columns per row. Let me reorganize by rows properly.
Actually, looking at the layout again — each row has two problems side by side. So we should pair them as:
Row 1: √225×√4 = 30 | √9×√625 = 75
Row 2: √64×√81 = 72 | √16×√144 = 48
Row 3: √4×√9 = 6 | √144×√4 = 24
Row 4: √9×√144 = 36 | √36×√144 = 72
Row 5: √49×√144 = 84 | √16×√64 = 32
Row 6: √144×√4 = 24 | √100×√16 = 40
Row 7: √144×√4 = 24 | √784×√16 = 112
Row 8: √25×√400 = 100 | √25×√100 = 50
Row 9: √25×√400 = 100 | √225×√4 = 30
Row 10: √64×√9 = 24 | √225×√9 = 45
Row 11: √196×√9 = 42 | √441×√9 = 63
Row 12: √9×√225 = 45 | √1×√16 = 4
Yes, that matches.
Final Answer:
30, 75, 72, 48, 6, 24, 36, 72, 84, 32, 24, 40, 24, 112, 100, 50, 100, 30, 24, 45, 42, 63, 45, 4
Parent Tip: Review the logic above to help your child master the concept of multiplying roots worksheet.
