7th Grade Math

54 Expressions and Patterns

The factors multiplied to form perfect squares are called square roots.

A radical sign, √ (^) a , is the symbol used to indicate a square root.
Square Root
Words A square root of a number is one of its two equal factors.
Examples Numbers Algebra
4 · 4 = 16, so √ 16  = 4. If x · x or x^2 = y, then^
(^) √ (^) 
y^ = x.
Find Square Roots
Find √81.
9 · 9 = 81, so √  81 = 9. What number times itself is 81?
Find √225.
[ √ (^)  ] 225 15
So, √ 225 = 15.
Find each square root.
d. √  64 e. √  289
SPORTS The infield of a
2nd base
Home plate
Pitcher’s
Mound
3rd base 1st base
baseball field is a square
with an area of 8,100
square feet. What are the
dimensions of the infield?
The infield is a square. By
finding the square root of
the area, 8,100, you find the
length of one side of the
infield.
90 · 90 = 8,100, so √ 8,100 = 90.
The dimensions of the infield are 90 feet by 90 feet.
f. SPORTS The largest ring in amateur boxing is a square with an
area of 400 square feet. What are the dimensions of the ring?
Square Roots
Read √  16 = 4 as the
square root of 16 is 4.
Real-World Link
The average number
of pitches for a major
league baseball is
7 pitches.
RR
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