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((

*x*1 -

*x*2)² + (

*y*1 -

*y*2)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.

## 1 comment:

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) ~= 9.2202) 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) ~= 3.606Here 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) ~= 5.0996) (3, 1) and (-5, -9)

Answer: sqrt((3--5)² + (1--9)²) =

sqrt(8² + 10²) =

sqrt(164) = 2sqrt(41) ~= 12.806Post a Comment