## 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)

#### 1 comment:

Prof. Hubbard said...

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)