Math Product Law of Radicals. Answer the questions with solutions and accurate answers.
3
1. Can the Product Law of Radicals be applied in simplifying √3*√3? Why or why not?
Solution/Explanation:
No, since they have different radicals. i.e, cube root and square root. But we can use the law of
exponent to calculate such expressions.
We know that ax ay =ax+y . In this case,
3
1
3
5
1
√3*√3 = (3)3 (3)2
√3*√3 = (3)6
3
6
√3*√3=√243
2. Explain why √-16*√-4=√64=8 is an incorrect application of the Product Law of Radicals.
Solution/Explanation:
The above operation is incorrect since a negative square root will result to imaginary numbers.
Hence, the proper implementation would be
√-16*√-4=(4i)(2i)
√-16*√-4=8i2
√-16*√-4=8(-1)
√-16*√-4=-8
3. Why do you think that √52 =5
Solution/Explanation:
No, this expression is incomplete. Since the square of negative 5 must be included. Hence, the
correct expression would be
√52 =|5|