Simplify 4/(5- square root of 13)

Problem

4/(5−√(,13))

Solution

1. Identify the conjugate of the denominator to rationalize the expression. The conjugate of 5−√(,13) is 5+√(,13)

2. Multiply both the numerator and the denominator by this conjugate.

4/(5−√(,13))⋅(5+√(,13))/(5+√(,13))

3. Expand the numerator and the denominator. In the denominator, use the difference of squares formula (a−b)*(a+b)=a2−b2

(4*(5+√(,13)))/(5−(√(,13))2)

4. Simplify the denominator by calculating the squares.

(4*(5+√(,13)))/(25−13)

5. Subtract the values in the denominator.

(4*(5+√(,13)))/12

6. Reduce the fraction by dividing both the numerator and the denominator by their greatest common factor, which is 4

(5+√(,13))/3

Final Answer

4/(5−√(,13))=(5+√(,13))/3

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