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How do I do this simple problem?
- Thread starter Centurion
- Start date
http://www.purplemath.com/modules/radicals.htm((2rad3)/3) x ((rad3)/2)
How do you multiply 2rad3 by rad3?
D
Deleted member 4993
Guest
Rewriting the hint above in LaText:
\(\displaystyle \sqrt{x} \ * \ \sqrt{x} \ = \ x\)
\(\displaystyle A \ * \ \sqrt{x} \ * \ \sqrt{x} \ = \ A \ * \ x\)
Then the answer to the question
is
The same way you multiply 2*3 by 3
\(\displaystyle \sqrt{x} \ * \ \sqrt{x} \ = \ x\)
\(\displaystyle A \ * \ \sqrt{x} \ * \ \sqrt{x} \ = \ A \ * \ x\)
Then the answer to the question
How do you multiply 2rad3 by rad3?
is
The same way you multiply 2*3 by 3
Last edited by a moderator:
another way to look at it is:
\(\displaystyle \sqrt{x} = x^{1/2}\), so
\(\displaystyle (a\sqrt{x})(b\sqrt{x}) = (ab)(\sqrt{x}\sqrt{x})\)
\(\displaystyle = (ab)(x^{1/2})(x^{1/2}) = (ab)(x^{(1/2 + 1/2)}) = (ab)x^1 = (ab)x\)
using the familar "laws of exponents".
for the time being, it's best to restrict such use (of exponent laws) to "rational exponents" and "non-negative x", for reasons which are too far off-topic to go in to.
\(\displaystyle \sqrt{x} = x^{1/2}\), so
\(\displaystyle (a\sqrt{x})(b\sqrt{x}) = (ab)(\sqrt{x}\sqrt{x})\)
\(\displaystyle = (ab)(x^{1/2})(x^{1/2}) = (ab)(x^{(1/2 + 1/2)}) = (ab)x^1 = (ab)x\)
using the familar "laws of exponents".
for the time being, it's best to restrict such use (of exponent laws) to "rational exponents" and "non-negative x", for reasons which are too far off-topic to go in to.