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)
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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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