SQUARE AND SQUARE ROOTS
SQUARE
Square number is the result of multiplying a number by itself. Example include:
2 x 2 = 2² = 4
3 x 3 = 3² = 9
4 x 4 = 4² = 16
Therefore, 4, 9, 16,... are square numbers because, these are numbers gotten from multiplying a number by itself.
How do you call it?;
2² { 2 raised to the power of 2 or 2-squared}
3² { 3 raised to the power of 2 or 3-squared}
Scroll down to view image with simplified calculation
EXAMPLE 1
Square Of Whole Numbers And Decimals
Evaluate each of the following;
(a) 220² (b) 0.7² (c) 10²
Solution
(a) 220² = 220 multiplied by itself
= 220 x 220
Answer = 48400
(b) 0.7² = 0.7 multiplied by itself
= 0.7 x 0.7
Answer = 0.49
(c) 10² = 10 multiplied by itself
= 10 x 10
Answer = 100
EXAMPLE 2
Square Of Fractions
Evaluate each of the following squared numbers;
(a) (5/11)² (b) (2'3/16)² (c) (2.7)²
Solution
The brackets means that all numbers inside it must be squared. Both the numerator and denominator.
(a) (5/11)² = (5 x 5)/(11 x 11)
Answer = 25/121
(b) (2'3/16)²
This is a mixed fraction. Convert to improper fraction to solve.
[2'3/16]² = [(16 x 2) + 3]/16
= (35/16)²
We have successfully converted the mixed fraction to improve fraction. They are still the same
[2'3/16]² is the same as (35/16)²
(35/16)² = (35 x 35)/(16 x 16)
= (1225/256)
Answer = 4'201/256
(c) (2.7)²
(2.7)² is also the same as (27/10)²
(27/10)² = (27 x 27)/(10 x 10)
= (729)/(100)
Answer = 7.29
SQUARE ROOT
Square root is the inverse (opposite) of squaring numbers.
12 x 12 = 144
√144 = √12 x 12 = 12.
EXAMPLE 1
Find the sqare root of the following numbers
(a) √400 (b) √900
Solution
There are different method you can use to find square root of numbers. But here is the simplest method. Factorization method.
View image for solution
(b)√900
View image for solution
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Tags:
Square and Square root