Multiplying Square Roots
For nonnegative numbers, the square root of a
product equals the product of the square
This is how you determine answers not on page
√18 = √9 ∙ 2 = √9 ∙ √2 = 3 ∙ √2
Isosceles Right Triangles also known as:
Use the degrees to identify these types of
C² = A² How 45-45-90 Triangles Work
+ B² ← Pythagorean Theorem
*Isosceles triangles have two equal length legs.*
Th e r e f o r e , A a n d B a r e t h e
s a m e le n g t h !
C² = 2x² ← the length of the leg is now
represented by x.
C = √2x² ← Undo the square on the c.
C = √2 ∙ √x² ← Multiplying Square Roots.
C = √2 ∙ x ← The hypotenuse of a 45-45-90
triangle is always √ multiplied by the length of
45-45-90 triangles Hypotenuse = leg x √2
have congruent leg
lengths and the
hypotenuse is the
length of the leg
multiplied by √2.
90° X 45°
What is the Square Root of 2?
√ = 1.41423562
So round answers to the nearest
tenth unless asked to do otherwise.
Two 30°-60°-90° triangles are
formed when you cut an
Equilateral Triangle in half.
The Hypotenuse of each
30-60-90 is twice the length
of the shorter leg.
Use Pythagorean Theorem to
find the length of the longer
30°-60°-90°: Determ Long Leg
C² = A² + B²
(2x)² = x² + B² ← B is the length of the long
4x² = x² + B²
3x² = B² ← Minus x²
√3x² = B ← Undo square root
√3 ∙ x = B ← Multiply square root
The length of the longer leg = the √ ∙ the
length of the shorter leg.