simplify the following (a) 2√2+4√7-3√2-4√7 (b) (√5+7)^
Answers
Answer:
Multiplying Radical Expressions
When multiplying radical expressions with the same index, we use the product rule for radicals. If a and b represent positive real numbers,
Example 1: Multiply:
√
2
⋅
√
6
.
Solution: This problem is a product of two square roots. Apply the product rule for radicals and then simplify.
Answer:
2
√
3
Example 2: Multiply:
3
√
9
⋅
3
√
6
.
Solution: This problem is a product of cube roots. Apply the product rule for radicals and then simplify.
Answer:
3
3
√
2
Often there will be coefficients in front of the radicals.
Example 3: Multiply:
2
√
3
⋅
5
√
2
.
Solution: Using the product rule for radicals and the fact that multiplication is commutative, we can multiply the coefficients and the radicands as follows.
Typically, the first step involving the application of the commutative property is not shown.
Answer:
10
√
6
Example 4: Multiply:
−
2
3
√
5
x
⋅
3
3
√
25
x
2
.
Solution:
Answer:
−
30
x