Question

8 класс
Упростите выражение
А)10√3-4√48-√75
Б)(5√2-√18)√2
В)(3-√2)^2
Г)(1+3√2)(3√2-1)

Answer 1

А)10√3-4√48-√75= 10√3-4√16×3-√25×3= 10√3-16√3-5√3=-11√3

Б)(5√2-√18)√2=(5√2-√2×9)√2=(5√2-3√2)√2= 5×2-3×2=4

В)(3-√2)²=9-6√2+2= 11-6√2

Г)(1+3√2)(3√2-1)=9×2-1=18-1=17

Answer 2

$10 \sqrt{3} -4 \sqrt{48}- \sqrt{75}=10 \sqrt{3} -4 \sqrt{16*3}- \sqrt{25*3}=10 \sqrt{3}-4*4 \sqrt{3}-$$-5 \sqrt{3}=10 \sqrt{3}-16 \sqrt{3}-5 \sqrt{3}=-11 \sqrt{3}$
$(5 \sqrt{2} - \sqrt{18})* \sqrt{2}=(5 \sqrt{2} - \sqrt{9*2})* \sqrt{2} =(5 \sqrt{2} -3 \sqrt{2})* \sqrt{2}=$$=2 \sqrt{2} * \sqrt{2}=2*( \sqrt{2}) ^{2} =2*2=4$
$(3- \sqrt{2}) ^{2} = 3 ^{2}-2*3* \sqrt{2}+( \sqrt{2}) ^{2} =9-6 \sqrt{2}+2=11-6 \sqrt{2}$
$(1+3 \sqrt{2})(3 \sqrt{2} -1)=(3 \sqrt{2} ) ^{2} -1 ^{2} =18-1=17$