# Squares and Square Roots - Mathematics Form 1

#### MATHEMATICS REVISION QUESTIONS

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## Squares

A square is the result of multiplying a number by itself.

### Squares by Multiplication

Find the Square of  a)  3 , b)  14 , c) 245
a) 32 = 3 x 3 = 9
b) 142 = 14 x 14 = 196
c) 2452 = 245 x 245 = 60025

### Squares using tables

Ensure you have a multiplication table to attempt these questions. Also note that the table of figures gives the answers correct to 4 Significant Figures
a) Find the square of 3.87 (3.872)
- In your table of figures, check where 38 intersects with 7. That is your figure.
- Ensure its 1498.
- Remember it is 2dp. Hence:
3.872 = 14.98
a) Find 0.037562
0.037562 = (3.756 x 0.01)2
0.037562 = 3.7562 x 0.0001
- In your table of figures, check where 37 intersects with . That is your figure.
- Ensure its 1406.
- On the same row, check the number intersecting with column number 6 (Right most column section labelled 'add')
- Ensure its 5.
- 1406 + 5 = 1411
- Remember it is 2dp. Hence:
0.037562 = 14.11 x 0.0001
= 0.001411

## Square Roots

Reverse of Square. Hence from the examples above the square root of 196 is 14 and the square root of 60025 is 245.

### Square root by factorization

Note: It is only used if the powers are even numbers
Find the square root of 7056
= 2 x 3528
= 2 x 2 x 1764
= 2 x 2 x 2 x 882
= 2 x 2 x 2 x 2 x 441
= 2 x 2 x 2 x 2 x 3 x 147
= 2 x 2 x 2 x 2 x 3 x 3 x 49
= 2 x 2 x 2 x 2 x 3 x 3 x 7 x 7
= 24 x 32 x 72
= 2(4 ÷ 2) x 3(2 ÷ 2) x 7(2 ÷ 2)
= 22 x 31 x 71
= 84

### Square root by using tables

Match the rows and columns just like in square. Always keep in mind the decimal places.

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