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PreAlgebra
STUDY GUIDE: Chapter 7: Real Numbers & Pythagorean Theorem
A square root of a number is a number that when multiplied by itself equals the given number. Every
positive number has a positive and a negative square root. A cube root of a number is a number that
when multiplied by itself 3 times , equals the given number. A negative number can have a cubed root.
1. What is √
16
1.
49
2. What is ± √
121
25
3
3
7
2. +/-
3. What is √−64
4. What is √
4
3.
27
5
-4
4. 3/6 = 1/2
216
5. Evaluate: 3√25 + 4
5.
19
6.
4
= 3*5 + 4 = 19
3
6. Evaluate: ( ½) √216
= ½ (8) = 4
11
Pythagorean Theory: a2 + b2 = c2
7. What is the missing length of the triangle:
6
x
7. 10
62 + 82 = c2
36 + 64 = c2
100 = c2
√100 = c
10 = c
8
Know the definition of rational, irrational, and rational integer on Page 310.
8. Is √64 rational, irrational, or rational integer
8. Rational int.
Estimating square roots: If a number does not have a perfect square, you
may have to estimate its square roots to either the nearest integer or nearest
10th place. Review pg 311.
9. Estimate the √83 to the nearest in integer
9._______9__________
The perfect square less than √83 = √81
The perfect square greater than √83 = √100
83 is only 2 away from 81, but is 17 away from 100, so answer is √81 = 9
10. Estimate the √83 to the nearest in tenth
10.____________
From question #9, we know it is close to √81, but greater than 9.
Try 9.12 1st: 9.1 x 9.1 = 82.81
Now try 9.22 : 9.2 x 9.2 = 84.64
So we have the decimal that is 1 below √81 and 1 above √81. Now see which
is closer.
83 – 82.81 = .19
84.64 – 83 = 1.64 so 9.1 is closer
11. Explain in the space below why this triangle either is or is not a right
triangle?
21
14
9
To answer this, determine if this is a right triangle. Remember in a right
triangle, the hypotenuse is the larges side, so test to see if
92 + 142 =?= 212
81 + 225 = ?= 441
306 does not equal 441 so it is not a right triangle.
12. What is the side length of a square that has an area 12._____14__________
of 196 cm2 ?
This is just the square root of 196 , √196 =14
13. What is the edge length of a cube that has a
volume of 343in3 ?
13.____7_________
This is the cubed root of 343 which equals 7
14. A right triangle has 2 sides that measure
5 inches and 12 inches. What is the length
of the hypotenuse?
14.____13_______
Do a2 + b2 = c2
52 + 122 = c2
25 + 144 = c2
169 = c2
c = √169 = 13
Distance Formula: d=
(x2 – x1)2 + (y2 – y1)2
15. Find the distance between (0,-5) , (4,1)
1st do (4-0)2 + (1 - -5)2 = 42 + 62 =
16 + 36 =
√52
15.____√52___