What is square root?
Square Roots are the inverse of squaring.
A square root can be thought of as a side in a square.
√S²= S
√12²= 12
√144= 12
What is a square number?
A number multiplied by itself.
SxS=S²
7x7=7²
7x7=49
You can find the approximate √ of a number using perfect squares. The whole number is the same as the smaller perfect square for all √ in between.
To estimate a fractional √ we can find the whole number. To find the denominator of the fraction subtract the perfect squares.
To find the numerator we count the √'s position between perfect squares.
Textbook Questions 3.3 :9, 14, 16
9. What are all possible whole numbers that have a square root between 4 and 5?
17, 18, 19, 20, 21, 22, 23, 24
14. Alex is thinking of a number. The number has a square root between 7 and 8, and it is a multiple of 12.
a) What number could he be thinking of?
60
b) Is there more than one answer? Explain
No because the number must be between 49 and 64. The only multiple of 12 in between 49 and 64 is 60.
16. A fitness centre will install a square hot tub in a 6 m x 6 m room. They want the tub to fill no more than 75% of the room's area
a) What is the maximum area of the hot tub?
SxS=a
6x6=36m²
0.75x36=27m²
b) What dimensions, to a tenth of a metre, will the fitness centre order from the manufacturer?
The fitness centre should order dimensions of 5.1 m by 5.1 m, so the area does not pass 75% of the space.
5.1x5.1=26.01
Pythagorean Relationship
1. The Pythagorean Relationship is the relationship between the side lengths of a right triangle . The hypotenuse is equal to the areas of the legs.
2. Solve the missing side length
c²= a²+b²c²= 12²+5²
c²= 144cm²+25cm²c²= 169cm²
√c²= √169cm² c= 13 cm
3. Is this a right triangle?
c²= a²+b²c²= 8²+6²
c²= 64cm²+36cm²
c²= 100cm²
√c²= √100cm²
c= 10 cm
No, it's not a right triangle because the legs don't equal the hypotenuse.
