November 5, 2021 CE

Roots

  1. How many legs does a right triangle have?

    Which sides join at the right angle?
    2

  2. What is the maximum number right angles a right triangle can have?

    The three interior angles of every triangle always add up to 180°.
    1

  3. In a right triangle, which side is always directly across from the right angle?

    Which side is longest?
    The hypotenuse, which is side $c$ in the Pythagorean Theorem.

  4. Is $\dfrac{3}{16}$ between $\dfrac{1}{8}$ and $\dfrac{1}{4}$?

    Convert all fractions to common denominators.
    Yes. $\dfrac{1}{8}=\dfrac{2}{16}$ and $\dfrac{1}{4}=\dfrac{4}{16}$

  5. Which of the following numbers is NOT a perfect square? $$ 1, 2, 3, 4, 5, 6, 7, 8, 9$$

    A perfect square is the product of an integer multiplied to itself, such as $2 \times 2 = 4$.
    $ 2, 3, 5, 6, 7, 8$

  6. What is the Pythagorean Theorem?

    The sum of the squares of the legs…
    $a^2 + b^2 = c^2$

  7. In a right triangle, which side is always the longest?

    In the Pythagorean Theorem ($a^2 + b^2 = c^2$), $c$ is always the hypotenuse.
    The hypotenuse

  8. Do the side lengths of $3$, $4$ and $5$ form a right triangle?

    $a^2 + b^2 = c^2$
    Yes. $3^2 + 4^2 = 5^2$

  9. Do the side lengths of $8$, $10$ and $14$ form a right triangle?

    $a^2 + b^2 = c^2$
    No. $8^2 + 10^2 \ne 14^2$

  10. Do the side lengths of $6$, $8$ and $10$ form a right triangle?

    $a^2 + b^2 = c^2$
    Yes. $6^2 + 8^2 = 10^2$

  11. What two integers are the square root $\sqrt{30}$ between?

    What are the roots of the closest perfect squares?
    5 and 6

  12. What two integers is the square root $\sqrt{42}$ between?

    What are the roots of the closest perfect squares?
    6 and 7

  13. What two integers is the square root $\sqrt{55}$ between?

    What are the roots of the closest perfect squares?
    7 and 8

  14. What two integers is the square root $\sqrt{67}$ between?

    What are the roots of the closest perfect squares?
    8 and 9

  15. To the nearest tenth, what is the missing side length of a right triangle when side $b=40$ and side $c=50$?

    $a^2 + b^2 = c^2$
    $a=30$

  16. To the nearest tenth, what is the missing side length of a right triangle when side $a=10$ and side $c=26$?

    $a^2 + b^2 = c^2$
    $b=24$

  17. To the nearest tenth, what is the missing side length of a right triangle when side $a=65$ and side $c=97$?

    $a^2 + b^2 = c^2$
    $b=72$