Properties of Square Root Radicals
The product of the square roots of two numbers is the same as the square root of their product.
a
b
a
b
7
3
7
3
21
■
The quotient of the square roots of two numbers is the square root of the quotient of the two numbers.
a
b
, where
b
≠
0
2
8
4
3
■
The square of a square root radical is the radicand.
(
N
)
2
N
(
4
)
2
4
4
16
4
■
When adding or subtracting radicals with the same radicand, add or subtract only the coefficients. Keep the
radicand the same.
a
b
c
b
(
a
c
)
b
4
7
6
7
(4
6)
7
10
7
■
You cannot combine radicals with different radicands using addition or subtraction.
a
b
≠
a
b
2
3
≠
5
■
To
simplify a square root radical, write the radicand
as the product of two factors, with
one number being
the largest perfect square factor. Then write the radical over each factor and simplify.
8
4
2
2
2
2
2
27
9
3
3
3
3
3
Practice Question
Which of the following is equivalent to 2
6
?
a.
2
3
3
b.
24
c.
d.
2
4
2
2
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