Square both sides of your original equation and then rationalize the denominator on the left side.terryds said:Homework Statement
If ##\sqrt{\frac{10+4\sqrt{6}}{10-4\sqrt{6}}}=a+b\sqrt{6}##, then a+b is ?
A) 8
B) 7
C) 6
D) 5
E) 4
The Attempt at a Solution
[/B]
This is my attempt:
##\sqrt{\frac{10+4\sqrt{6}}{10-4\sqrt{6}}}=\sqrt{\frac{10+4\sqrt{6}*(10+4\sqrt{6})}{10-4\sqrt{6}*(10+4\sqrt{6})}}=\sqrt{\frac{196+80\sqrt{6}}{4}}=\sqrt{49+20\sqrt{6}}##
Then, I got stuck.. I have no idea how to convert to form a+b√6
Please help..
You have to use parentheses. The correct form is ##\sqrt{\frac{10+4\sqrt{6}}{10-4\sqrt{6}}}=\sqrt{\frac{(10+4\sqrt{6})*(10+4\sqrt{6})}{(10-4\sqrt{6})*(10+4\sqrt{6})}}##terryds said:This is my attempt:
##\sqrt{\frac{10+4\sqrt{6}}{10-4\sqrt{6}}}=\sqrt{\frac{10+4\sqrt{6}*(10+4\sqrt{6})}{10-4\sqrt{6}*(10+4\sqrt{6})}}=\sqrt{\frac{196+80\sqrt{6}}{4}}=\sqrt{49+20\sqrt{6}}##
.
Thanks.. a is 5 and b is 2 , so a+b is 7..Mark44 said:√
Square both sides of your original equation and then rationalize the denominator on the left side.
You should get something like m + n√(6) on one side and r + s√(6) on the other side. You can equate m with r and n with s to get two equations involving a and b.
Rationalizing a complex root means simplifying it so that the denominator is a rational number (a number that can be expressed as a fraction). This is typically done by multiplying both the numerator and denominator by the conjugate of the complex root.
Rationalizing complex roots can help us simplify complex expressions and make them easier to work with. It also helps us to find the exact solutions for equations involving complex numbers.
No, not all complex roots can be rationalized. Only complex roots with a denominator that is a surd (a root that cannot be simplified) can be rationalized.
Rationalizing a complex root involves changing the form of the expression by multiplying it by the conjugate of the root, while simplifying involves reducing the expression to its simplest form. Rationalizing a complex root often leads to a simpler expression, but it is not always the case.
Yes, there are other methods for simplifying complex roots, such as using the quadratic formula or completing the square. However, rationalizing is the most common method used to simplify complex roots.