question 30 (1 point) which of the following expresses (4 - √7)(5 + √60) in simplest form? a) 20 + 8√15…

question 30 (1 point) which of the following expresses (4 - √7)(5 + √60) in simplest form? a) 20 + 8√15 - 5√7 - 2√105 b) 20 + 40√6 - 5√7 - 10√42 c) 20 - 2√105 d) -21√97

question 30 (1 point) which of the following expresses (4 - √7)(5 + √60) in simplest form? a) 20 + 8√15 - 5√7 - 2√105 b) 20 + 40√6 - 5√7 - 10√42 c) 20 - 2√105 d) -21√97

Answer

Explanation:

Step1: Expand the product using FOIL method

[ \begin{align*} (4 - \sqrt{7})(5+\sqrt{60})&=4\times5+4\times\sqrt{60}-\sqrt{7}\times5-\sqrt{7}\times\sqrt{60}\ &=20 + 4\sqrt{4\times15}- 5\sqrt{7}-\sqrt{7\times4\times15}\ &=20+8\sqrt{15}-5\sqrt{7}-2\sqrt{105} \end{align*} ]

Answer:

a) (20 + 8\sqrt{15}-5\sqrt{7}-2\sqrt{105})