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parry
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5+2 root 6 / 7+4root3 = a-b root3 find a and b
Rationalizing an expression means to eliminate any irrational numbers in the expression, such as square roots or cube roots, by manipulating the expression in a way that the final result is a rational number (a number that can be expressed as a ratio of two integers).
To rationalize this expression, we need to eliminate the irrational number in the denominator, 4√3. To do this, we can multiply both the numerator and denominator by the conjugate of 7+4√3, which is 7-4√3. This will result in a difference of squares, allowing us to eliminate the radical in the denominator. The final rationalized expression is (35-20√2)/(49-48) = (35-20√2)/1 = 35-20√2.
Rationalizing expressions is important because it allows us to simplify and manipulate expressions in a way that is easier to work with and understand. It also allows us to find exact solutions to problems, rather than having to work with decimal approximations.
No, not all expressions can be rationalized. Only expressions with irrational numbers in the denominator, such as square roots or cube roots, can be rationalized. Expressions with other types of irrational numbers, such as π or e, cannot be rationalized.
Yes, there are other methods to rationalize expressions, such as using the rationalizing factor method or the completing the square method. These methods may be more useful in certain situations, so it is important to understand and be familiar with multiple methods of rationalizing expressions.