Here are the answers to the 3 Pythagoras Questions.
Explanation: the two legs of the right triangle are a² and b²; a² and b² add up to the hypotenuse which is what c². If the two legs (a² and b²) do not add up to the hypotenuse (c²) then it is not considered a right triangle.
Steps: You add a ² and b² ( 12² and 5² or 144 cm² and 25cm²) and that would get you c² which is 169 cm². Then you take 169 cm ² and square it which would get you the side length (13 cm). So the length of c is 13cm.
Explanation: No, this triangle is not a right triangle, because if you did the calculations the two legs would not add up to the hypotenuse.
Text Book (Pages 98-100)
Questions 17, 18, 21
Question # 17
A. You get the area of the bored by multiplying the two side lengths of the square picture. So it would be 18 x 18 = 324 . So the area is 324 cm²
B.To get the area of the board you have to multiply the area of the picture by 4, because it says that the board is 4 times the size of picture. ( 324 x 4 = 1296m) 1296 cm².
C. To get the dimension of the board and or side length you have to find the square root of 1296 cm² which is 36 cm. You can get the square root of 1296 cm² by using the square root button on your calculator and it will give you the 36 cm as the square root of 1296 cm². Or you can use a factorization tree.
Question # 18
A. You can get the square root of 9 two different ways, you can use a prime factorization tree or you can use the square root button on your calculator. When you use a prim factorization tree you have to find two identical numbers that you can multiple together to get the number 9, so for this question it would be 3 (3 x 3 = 9)
B.To estimate what square root of 3 you make a number line and find the two closes perfect squares to the number, so for this question it would be 4 and 1, you mark where the half way point is on the number line and then you have to find out if 3 is closer to the numbers 1 or 4. It's closer to the number 4. 3 is smaller then 4 so the whole number that comes before the decimal would have to be a 1, so the square root of 3 would have to be 1.__ .
C.To get the square root of 3 you can easily use the square root button on your calculator. If you typed it in right you should have 1.732050808 as the square root of 3. But the question is asking you to express the number to the nearest hundredth so it would be shorten to 1.73.
D. This question is pretty self explanatory, all you have to do is compare your estimate in part b) to the calculation to part c).
Question # 21
You can answer this question by first finding out which two numbers have the square root of 326² and 327². You can find out these two numbers by multiplying each one of the numbers by them selves (326 x 326 = 102 276) and (327 x327 = 106 929). So now you have to find out what numbers between 106 276 and 106 929 are divisible by 100 and are multiples of six. When finding these numbers you can easily eliminate numbers that don't end with zeros; because those numbers wouldn't be multiples of 100. So now you're left with the numbers 106 300, 106 400, 106 500, 160 600, 160 700, 160 800, 160 900. Then you divide all those numbers one by one by six (106 300 ÷ 6 = 17716.666667 etc.) You'll find out if the number is divisible by 6 if you multiple it by six and it still stays a whole number.
Here is a video that might help you do some square rooting:
Here is a link that will help you practice some square roots: http://www.funbrain.com/tictactoe/index.html
Click squares on either the easy, medium or hard section to proceed on playing the the game.