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Roots

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Keywords: Roots

Questions

1.
How many legs does a right triangle have?
Hint: Which sides join at the right angle?
 
2.
What is the maximum number right angles a right triangle can have?
Hint: The three interior angles of every triangle always add up to 180°.
 
3.
In a right triangle, which side is always directly across from the right angle?
Hint: Which side is longest?
 
4.
Is $\dfrac{3}{16}$ between $\dfrac{1}{8}$ and $\dfrac{1}{4}$?
Hint: Convert all fractions to common denominators.
 
5.

Which of the following numbers is NOT a perfect square?

$$ 1, 2, 3, 4, 5, 6, 7, 8, 9$$
Hint: A perfect square is the product of an integer multiplied to itself, such as $2 \times 2 = 4$.
 
6.
What is the Pythagorean Theorem?
Hint: The sum of the squares of the legs…
 
7.
In a right triangle, which side is always the longest?
Hint: In the Pythagorean Theorem ($a^2 + b^2 = c^2$), $c$ is always the hypotenuse.
 
8.
Do the side lengths of $3$, $4$ and $5$ form a right triangle?
Hint: $a^2 + b^2 = c^2$
 
9.
Do the side lengths of $8$, $10$ and $14$ form a right triangle?
Hint: $a^2 + b^2 = c^2$
 
10.
Do the side lengths of $6$, $8$ and $10$ form a right triangle?
Hint: $a^2 + b^2 = c^2$
 
11.
What two integers are the square root $\sqrt{30}$ between?
Hint: What are the roots of the closest perfect squares?
 
12.
What two integers is the square root $\sqrt{42}$ between?
Hint: What are the roots of the closest perfect squares?
 
13.
What two integers is the square root $\sqrt{55}$ between?
Hint: What are the roots of the closest perfect squares?
 
14.
What two integers is the square root $\sqrt{67}$ between?
Hint: What are the roots of the closest perfect squares?
 
15.
To the nearest tenth, what is the missing side length of a right triangle when side $b=40$ and side $c=50$?
Hint: $a^2 + b^2 = c^2$
 
16.
To the nearest tenth, what is the missing side length of a right triangle when side $a=10$ and side $c=26$?
Hint: $a^2 + b^2 = c^2$
 
17.
To the nearest tenth, what is the missing side length of a right triangle when side $a=65$ and side $c=97$?
Hint: $a^2 + b^2 = c^2$
 
Possible Points: 0

Questions

1.
How many legs does a right triangle have?
Hint: Which sides join at the right angle?
 
2.
What is the maximum number right angles a right triangle can have?
Hint: The three interior angles of every triangle always add up to 180°.
 
3.
In a right triangle, which side is always directly across from the right angle?
Hint: Which side is longest?
 
4.
Is $\dfrac{3}{16}$ between $\dfrac{1}{8}$ and $\dfrac{1}{4}$?
Hint: Convert all fractions to common denominators.
 
5.

Which of the following numbers is NOT a perfect square?

$$ 1, 2, 3, 4, 5, 6, 7, 8, 9$$
Hint: A perfect square is the product of an integer multiplied to itself, such as $2 \times 2 = 4$.
 
6.
What is the Pythagorean Theorem?
Hint: The sum of the squares of the legs…
 
7.
In a right triangle, which side is always the longest?
Hint: In the Pythagorean Theorem ($a^2 + b^2 = c^2$), $c$ is always the hypotenuse.
 
8.
Do the side lengths of $3$, $4$ and $5$ form a right triangle?
Hint: $a^2 + b^2 = c^2$
 
9.
Do the side lengths of $8$, $10$ and $14$ form a right triangle?
Hint: $a^2 + b^2 = c^2$
 
10.
Do the side lengths of $6$, $8$ and $10$ form a right triangle?
Hint: $a^2 + b^2 = c^2$
 
11.
What two integers are the square root $\sqrt{30}$ between?
Hint: What are the roots of the closest perfect squares?
 
12.
What two integers is the square root $\sqrt{42}$ between?
Hint: What are the roots of the closest perfect squares?
 
13.
What two integers is the square root $\sqrt{55}$ between?
Hint: What are the roots of the closest perfect squares?
 
14.
What two integers is the square root $\sqrt{67}$ between?
Hint: What are the roots of the closest perfect squares?
 
15.
To the nearest tenth, what is the missing side length of a right triangle when side $b=40$ and side $c=50$?
Hint: $a^2 + b^2 = c^2$
 
16.
To the nearest tenth, what is the missing side length of a right triangle when side $a=10$ and side $c=26$?
Hint: $a^2 + b^2 = c^2$
 
17.
To the nearest tenth, what is the missing side length of a right triangle when side $a=65$ and side $c=97$?
Hint: $a^2 + b^2 = c^2$
 
Possible Points: 0
 

Solutions

  1. 2
  2. 1
  3. The hypotenuse, which is side $c$ in the Pythagorean Theorem.
  4. Yes. $\dfrac{1}{8}=\dfrac{2}{16}$ and $\dfrac{1}{4}=\dfrac{4}{16}$
  5. $ 2, 3, 5, 6, 7, 8$
  6. $a^2 + b^2 = c^2$
  7. The hypotenuse
  8. Yes. $3^2 + 4^2 = 5^2$
  9. No. $8^2 + 10^2 \ne 14^2$
  10. Yes. $6^2 + 8^2 = 10^2$
  11. 5 and 6
  12. 6 and 7
  13. 7 and 8
  14. 8 and 9
  15. $a=30$
  16. $b=24$
  17. $b=72$
  18. 2
  19. 1
  20. The hypotenuse, which is side $c$ in the Pythagorean Theorem.
  21. Yes. $\dfrac{1}{8}=\dfrac{2}{16}$ and $\dfrac{1}{4}=\dfrac{4}{16}$
  22. $$ 2, 3, 5, 6, 7, 8$$
  23. $a^2 + b^2 = c^2$
  24. The hypotenuse
  25. Yes. $3^2 + 4^2 = 5^2$
  26. No. $8^2 + 10^2 \ne 14^2$
  27. Yes. $6^2 + 8^2 = 10^2$
  28. 5 and 6
  29. 6 and 7
  30. 7 and 8
  31. 8 and 9
  32. $a=30$
  33. $b=24$
  34. $b=72$