Question

Aduceti la forma cea mai simpla expresia:
a)$\sqrt{45}+ \sqrt{61 \frac{1}{4} } -11 \sqrt{1 \frac{1}{4}$
b)$( \sqrt{7} +4 \sqrt{3} + \sqrt{7} -4 \sqrt{3} ) ^{2}$
la punctub b la ambii 7 e radical mare
Va rooooooooooooooooooog urgent

Answer 1

√45+√61 1/4 -11√ 1 1/4=
=3√5+√245/4-11√5/4=
=3√5+(7√5)/2-(11√5)/2=
=(6√5+7√5-11√5)/2=
=2√5/2=√5

la b) aplicam formula radicalilor compusi
√(7+4√3)=√(7+√48)=√(7+√49-48)/2+√(7-√49-48)/2=
=√(7+1)/2+√(7-1)/2=√4+√3=2+√3

√(7-4√3)=√(7+√48)=√(7+√49-48)/2-√(7-√49-48)/2=
=√(7+1)/2-√(7-1)/2=√4-√3=2-√3

[√(7+4√3)+√(7-4√3)]²=(2+√3+2-√3)²=2²=4