Prealgebra: Decimals
Name: ____________________________________________ Topic E6: Square Roots and the Pythagorean Theorem | VERSION A Simplify the following expressions without using a calculator. 1.
49 = 2.
2 25 = 3.
3 64 = 4.
7.
64 − 16 = 8.
4 36 + 2 25 = 9.
4 36 − 5 16 = 5 16 = 10. 5.
7 49 = 6.
49 + 25 = 11. !
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Name: ____________________________________________ Topic E6: Square Roots and the Pythagorean Theorem | VERSION A Use a calculator to approximate the following square roots to the nearest thousandth. 12. 2 2 = 13. 14. !
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17. Find the length of the hypotenuse, 𝑐 , for the right triangle with sides, 𝑎 = 4 and 𝑏 = 9. Round to the nearest hundredth. 𝑐 = = !
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= 15. 𝑎 . 50 + 8 = 𝑏 . 58 = 𝑐 . 5 2 + 2 2 = 18. Find the length of the hypotenuse, 𝑐 , for the right triangle with sides, 𝑎 = 8 and 𝑏 = 8. Round to the nearest hundredth. 𝑐 = 19. One end of a wire is attached to the top of a 24-­‐foot pole; the other end of the wire is anchored to the ground 18 feet from the bottom of the pole. If the pole makes an angle of 90∘ with the ground, find the length of the wire. The length of the wire is _________________ feet. 𝑑 . 7 2 = 16. Find the length of the hypotenuse, 𝑐 , for the right triangle with sides, 𝑎 = 9 and 𝑏 = 12. 𝑐 = 20. Two children are trying to cross a stream. They want to use a log that goes from one bank to the other. If the left bank is 5 feet higher than right bank and the stream is 12 feet wide, how long must a log be to just barely reach? The log must be ____________________ feet. www.varsitylearning.com 2 Prealgebra: Decimals
Name: ____________________________________________ Topic E6: Square Roots and the Pythagorean Theorem | VERSION A Simplify the following expressions without using a calculator. 1.
49 = 7 2.
2 25 = 10 3.
3 64 = 24 4.
7.
64 − 16 = 4 8.
4 36 + 2 25 = 34 9.
4 36 − 5 16 = 4 5 16 = 20 10. 5.
6.
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7 49 = 49 49 + 25 = 12 11. !"!
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www.varsitylearning.com 3 Prealgebra: Decimals
Name: ____________________________________________ Topic E6: Square Roots and the Pythagorean Theorem | VERSION A Use a calculator to approximate the following square roots to the nearest thousandth. 12. 2 2 = 2.828 13. 14. !
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17. Find the length of the hypotenuse, 𝑐 , for the right triangle with sides, 𝑎 = 4 and 𝑏 = 9. Round to the nearest hundredth. 𝑐 = 9.85 = 0.447 !
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= 0.447 15. 𝑎 . 50 + 8 = 9.899 𝑏 . 58 = 7.616 𝑐 . 5 2 + 2 2 = 9.899 18. Find the length of the hypotenuse, 𝑐 , for the right triangle with sides, 𝑎 = 8 and 𝑏 = 8. Round to the nearest hundredth. 𝑐 = 11.31 19. One end of a wire is attached to the top of a 24-­‐foot pole; the other end of the wire is anchored to the ground 18 feet from the bottom of the pole. If the pole makes an angle of 90∘ with the ground, find the length of the wire. The length of the wire is 30 feet. 𝑑 . 7 2 = 9.899 16. Find the length of the hypotenuse, 𝑐 , for the right triangle with sides, 𝑎 = 9 and 𝑏 = 12. 𝑐 = 15 20. Two children are trying to cross a stream. They want to use a log that goes from one bank to the other. If the left bank is 5 feet higher than right bank and the stream is 12 feet wide, how long must a log be to just barely reach? The log must be 13 feet. www.varsitylearning.com 4