Select the answer which is equivalent to the given expression using your calculator. (13)/(-20+sqrt15) (-260+13sqrt15)/(385) (-20-sqrt15)/(385) (-260-13sqrt15)/(385) (-20+sqrt15)/(385)

Question

Select the answer which is equivalent to the given expression using your calculator.  (13)/(-20+sqrt15)  (-260+13sqrt15)/(385)  (-20-sqrt15)/(385)  (-260-13sqrt15)/(385)  (-20+sqrt15)/(385)

Bytelearn · Accepted Answer

Calculate Denominator: Calculate the denominator (-20+sqrt15) using a calculator.Rationalize Denominator: Since we are looking for an equivalent expression, we need to rationalize the denominator of the given expression. To do this, we multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of (-20+sqrt15) is (-20-sqrt15).Multiply Numerator: Multiply the numerator (13) by the conjugate of the denominator (-20-sqrt15). 13 * (-20-sqrt15) = -260 - 13sqrt15Multiply Denominator: Multiply the denominator (-20+sqrt15) by its conjugate (-20-sqrt15). (-20+sqrt15) * (-20-sqrt15) = (-20)^2 - (sqrt15)^2Calculate Squares: Calculate the squares of -20 and sqrt15. (-20)^2 = 400 (sqrt15)^2 = 15Subtract Squares: Subtract the square of sqrt15 from the square of -20. 400 - 15 = 385Write Expression: Write the expression with the calculated numerator and denominator. (-260 - 13sqrt15) / 385Compare with Options: Compare the result with the given options to find the equivalent expression. The equivalent expression is (-260 - 13sqrt15) / 385.Confirm Match: Confirm that the expression matches one of the given options. The expression (-260 - 13sqrt15) / 385 matches the option ＂(-260-13sqrt15)/(385)＂.

Select the answer which is equivalent to the given expression using your calculator. $\newline$ $\frac{13}{-20+\sqrt{15}}$ $\newline$ $\frac{-260+13 \sqrt{15}}{385}$ $\newline$ $\frac{-20-\sqrt{15}}{385}$ $\newline$ $\frac{-260-13 \sqrt{15}}{385}$ $\newline$ $\frac{-20+\sqrt{15}}{385}$

Full solution

More problems from Multiplication with rational exponents

Related topics