Textbook Questions 4, 8, and 9

4. Estimate the square root of each number, to one decimal place. Check your answer with calculator.

A.)
Square root of 72 is close to the halfway point of 66 and its square root is 8.1 and 72 is 4 numbers away from it. So the whole is 8 and the decimal is 4.
B.)

The square root of 103 is 10.1. For the whole it hasn't reach pass 11 so it is 10 and for the decimal I just counted how far it is from.
C.)
The square root of 55 is 7.5. for the Whole once again it has now pass 64 so therefore it is 7 and for the decimal I just rounded 49 by 50 then counted how far 50 is from 55 and I got 5.

8.) Identify all possible whole numbers with a square root larger that 2 and smaller than 3
2x2=4
3x3=9
5,6,7,8

9.) Identify all possible whole numbers that have a square root between 4 and 5.

4x4=16
5x5=25
17,18,19,20,21,22,23,24

Textbook Questions 14, 15, and 17

14. Alex is thinking of a number. The number has a square root between 7 and 8, and a multiple of 12.

a) What number could he be thinking of?

b) Is there more than one answer? Explain.

No, because 60 is the only number that is between the square root of 7 and 8 that is a multiple of 12.

15. Order the following numbers from least to greatest:

Ordered from least to greatest:

17. Carmel wants to mount an 18cm x 18cm square picture on a square board that is four times the area or the picture

a) What is the area of the picture?

324cm(squared)

b) What is the area of the board?

I got this answer because I multiplied 324cm(squared) by 4.

c) What are the dimensions of the board?

Play Mangahigh

Here's a video that can help.

Casey's Scribe Post- Estimate Square Roots

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+b²
c²= 12²+5²
c²= 144cm²+25cm²
c²= 169cm²
√c²= √169cm²
c= 13 cm

3. Is this a right triangle?


c²= a²+b²
c²= 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.