Sunday, July 3, 2011

Practice with square roots for homework due July 6.

The editor for Blogger doesn't have a square root sign available, so I will use sqrt(2) to signify the square root of 2, for example.



Here are two sides of a right triangle.  In these problems, c is always the hypotenuse and a and b are the short sides, also called the legs.  Find the missing side using the Pythagorean Theorem, write it as a square root in simplified form and give the approximation to the nearest thousandth.

1)  a = 7, b = 6, c = _________

2) b = 6, c = 7, a = __________

Here are some fractions with the square root in the denominator.  Write them in standard form and simplify.

3) 20/sqrt(10)

4) 15/sqrt(6)


Find the distance between the two given points using the formula Distance = sqrt((x1 - x2)² + (y1 - y2)²). Write the number as a square root in simplified form and give the approximation to the nearest thousandth.

5)  (3, 7) and (-2, 6)

6) (3, 1) and (-5, -9)

Answers in the comments.
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1 comment:

  1. Prof. HubbardJuly 3, 2011 at 10:29 AM

    Here are two sides of a right triangle. In these problems, c is always the hypotenuse and a and b are the short sides, also called the legs. Find the missing side using the Pythagorean Theorem, write it as a square root in simplified form and give the approximation to the nearest thousandth.

    1) a = 7, b = 6, c = _________

    Answer: 7² + 6² = 49 + 36 = 85
    85 = 5*17, so there are no perfect squares in its prime factorization.
    The length is sqrt(85) ~= 9.220

    2) b = 6, c = 7, a = __________


    Answer: 7² - 6² = 49 - 36 = 13
    13 is prime, so there are no perfect squares in its prime factorization.
    The length is sqrt(13) ~= 3.606

    Here are some fractions with the square root in the denominator. Write them in standard form and simplify.

    3) 20/sqrt(10)

    Answer: Multiply by sqrt(10)/sqrt(10) to get 20sqrt(10)/10 which simplifies to 2sqrt(10).

    4) 15/sqrt(6)

    Answer: Multiply by sqrt(6)/sqrt(6) to get 15sqrt(6)/6 which simplifies to 5sqrt(6)/2.


    Find the distance between the two given points using the formula Distance = sqrt((x1 - x2)² + (y1 - y2)²). Write the number as a square root in simplified form and give the approximation to the nearest thousandth.

    5) (3, 7) and (-2, 6)

    Answer: sqrt((3--2)² + (7-6)²) =
    sqrt(5² + 1²) =
    sqrt(26) ~= 5.099

    6) (3, 1) and (-5, -9)

    Answer: sqrt((3--5)² + (1--9)²) =
    sqrt(8² + 10²) =
    sqrt(164) = 2sqrt(41) ~= 12.806

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