10-1 The Pythagorean Theorem
Quick Review
Given th e lengths of two sides of a right triangle, you can
use the Pythagorean Theorem to find the length of the
third side. Given the lengths of all three sides of a triangle,
you can d eterm ine w h eth er it is a right triangle.Example
What is the side length x in the
triangle at the right? 15
a2 + b2 = c2 Pythagorean Theorem
152 + x 2 = 392 Substitute 15 fo r a, x for b, and 39 for c.
225+ jc2 = 1521 Simplify.
x2 = 1296 Subtract 225 from each side.
x = 36 Find the principal square root o f each side.Exercises
Use the triangle at the right. Find the
missing side length. If necessary, round to
the nearest tenth. ab6. a = 2.5, b = 6 7. a = 3.5, b= 128. a = 1.1, b = 6 9. a = 13, c = 85- a = 6, c = 18.5 11. b = 2.4, c = 2.5
- b = 8.8, c = 11 13. a = 1, c — 2.6
Determine whether the given lengths can be side lengths
of a right triangle. - 4, 7.5, 8.5 15.22,120,122 16.8,40,41
- 1.6, 3, 3.4 18.6,24,25 19.18,52.5,55.5
20. 1.2, 6, 6.1 21.0.7,2.3,2.5 22.1.3,8.4,8.510-2 Simplifying Radicals
Quick Review
A radical expression is sim plified if th e following
statem ents are true.- The radicand has no perfect-square factors o th er th a n 1.
- The radicand contains no fractions.
- No radicals ap p ear in th e d en o m in ato r of a fraction.
V$x„Example
What is the simplified form of
V3x V3x V2 u. - , V2
vT 'W t? “ P'vb»^r
Vfa
Vi
VtoMultiply numerators and denominators.Simplify.Exercises
Simplify each radical expression.- 3 VTi • ( - 2 V 2 I)
25.- V 8 • |V 6
25 a 3
4 a 26.
V 8 s
Vl8^3- -2 V7X2 • 28x3 28. 6 V 5 t ^ • Vl5t^
- Open-Ended Write th ree radical expressions th at
have 4 V2s as th eir sim plified form. W hat do the
th ree expressions have in com m on? Explain. - Geometry The w idth of a rectangle is s. Its length is
3s. How long is a diagonal of the rectangle? Express
your answ er in sim plified radical form.
654 Chapter 10 Ch ap t er Review