Question

simplify the following expressions.
1) (5+?7)(2+?5)
2) (5+?5)(5-?5)
3) (?3+?7)whole square
4) (?11-?7)(?11+?7)

Answer 1

Dear student,

$$\begin{gathered} Simplifythefollowingexpressions \\ 1)\left(5+\sqrt{7}\right)\left(2+\sqrt{5}\right) \\ solution: \\ =5\times 2+5\sqrt{5}+2\sqrt{7}+\sqrt{7}\times \sqrt{5} \\ =10+5\sqrt{5}+2\sqrt{7}+\sqrt{35} \\ 2)\left(5+\sqrt{5}\right)\left(5-\sqrt{5}\right) \\ solution: \\ u\sin g\left(a+b\right)\left(a-b\right)=a^2-b^2 \\ \left(5+\sqrt{5}\right)\left(5-\sqrt{5}\right)=5^2-{\left(\sqrt{5}\right)}^2 \\ =25-5 \\ =20 \\ 3){\left(\sqrt{3}+\sqrt{7}\right)}^2 \\ solution: \\ {\left(\sqrt{3}+\sqrt{7}\right)}^2={\left(\sqrt{3}\right)}^2+{\left(\sqrt{7}\right)}^2+2\times \sqrt{3}\times \sqrt{7} \\ =3+7+2\sqrt{21} \\ =10+2\sqrt{21} \\ 4)\left(\sqrt{11}-\sqrt{7}\right)\left(\sqrt{11}-\sqrt{7}\right) \\ solution: \\ u\sin g\left(a+b\right)\left(a-b\right)=a^2-b^2 \\ \left(\sqrt{11}-\sqrt{7}\right)\left(\sqrt{11}-\sqrt{7}\right)={\left(\sqrt{11}\right)}^2-{\left(\sqrt{7}\right)}^2 \\ =11-7 \\ =4 \end{gathered}$$

Regards