Squares and Square Roots

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.