Question

(1) 3√а-2√а (2) √с+10√с-14√с (3) 9√6-2√3+8√3-3√6

Answer 1

В первом примере выносим за скобки $\sqrt{a}$. Получаем:
$3 \sqrt{a} -2 \sqrt{a} = \sqrt{a} *(3-2)= \sqrt{a} *1= \sqrt{a}$
Во втором примере также выносим $\sqrt{c}$ за скобки:
$\sqrt{c} +10 \sqrt{c}-14 \sqrt{c} = \sqrt{c} *(1+10-14)= \sqrt{c} *(11-14)= \sqrt{c}*(-3)\\ =-3 \sqrt{c}$
В третьем примере группируем, вынося $\sqrt{6}$ и $\sqrt{3}$ за скобки:
$9 \sqrt{6} -2 \sqrt{3} +8 \sqrt{3} -3 \sqrt{6} = \sqrt{6} *(9-3)+ \sqrt{3} *(8-2)= \sqrt{6} *6+\\ + \sqrt{3} *6= \sqrt{6* 6^{2} } + \sqrt{3* 6^{2} } = \sqrt{ 6^{3} } + \sqrt{3*4* 3^{2} } =\\ =\sqrt{ 6^{3} } +2 \sqrt{ 3^{3} }$

Answer 2

1. To simplify 3√а-2√а, we can combine the terms that have the same square root of a: 3√а - 2√а = √а + √а + √а - 2√а Simplifying the right side of the equation gives us: √а

Therefore, 3√а-2√а simplifies to √a.

2. To simplify √с+10√с-14√с, we can again combine the terms that have the same square root of c: √с + 10√с - 14√с = (√с - 4√с) + 10√с Simplifying the right side of the equation gives us: -3√c

Therefore, √c+10√c-14√c simplifies to -3√c.

3. To simplify 9√6-2√3+8√3-3√6, we can again combine the terms that have the same square root of either 6 or 3: 9√6 - 2√3 + 8√3 - 3√6 = (9 - 3)√6 + (8 - 2)√3 Simplifying the right side of the equation gives us: 6√6 + 6√3

Therefore, 9√6-2√3+8√3-3√6 simplifies to 6√6 + 6√3.