Square Roots Worksheet Page 2
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1
2Square Roots containing Variables and Exponents
When a square root contains variables with exponents, divide the exponent by the index to find out
what you can bring out. Any remainder that is left stays under the radical sign.
4
2
x
x
If the index of the square root is 2, divide 2 into the
exponents. If the index of the square root is 3, divide 3 into
5 4
2 2
x y
x y
x
the exponents. Any remainders stay under the radical sign.
6 8
2 2
2
3
8
x y
2
x y
y
Multiplying Square Roots
You can only multiple the outside numbers together and the numbers under the radial sign together;
never the outside number with a number under the radical sign.
7
3
21
3 5 4 3
12 15
2 3 3 5 5 7
6 15 10 21
Using Foil to Multiply Square Roots: Multiply the outside numbers and the square root numbers. After
multiplying, reduce your square roots, remembering to multiply the square root you are taking out with
whatever is already outside the square root. Add any like terms.
3 5 2 3 4 5 3 9
1. Multiply the two binomials using FOIL.
12 25 9 45 8 15 6 27
2. Determine what terms are perfect squares.
12 5 5 9 9 5 8 15 6 9 3
3. Multiply the perfect square by any number
12(5) 9(3) 5 8 15 6(3) 3
that is outside the radical.
4. Simplify by combining any like terms.
60 27 5 8 15 18 3
If you do not know what the square root of a number is, you can use the prime factorization method to
find the square root.
2 35
140 = 2 x 2 x 5 x 7
The square root is
. The 2s show up twice so we can bring out a 2. The
rest is multiplied together and stays under the radical sign.
240 = 2 x 2 x 2 x 2 x 3 x 5 The square root is
4 15
We have two pairs of 2s, so we bring each one out
one time and multiply them together. The remainder stays under the radical
sign.
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