Question

3)a√x+b√x-m√x-b√x 2)2√a+3√a-4√a 4)√49с-√16с+√25с 5)2√18a+0,5√72b-√98a+√8b 6)5√2a-0,4√125k-√32a+√500k 6)√75-√147+0,75√48 7)√275-10√11-√99

Answer 1

3) $\displaystyle a \sqrt{x}+b \sqrt{x} -m \sqrt{x} -b \sqrt{x} = \sqrt{x} (a+b-m-b)=(a-m) \sqrt{x}$

2) $\displaystyle 2 \sqrt{a}+3 \sqrt{a}-4 \sqrt{a}= \sqrt{a}=(2+3-4)* \sqrt{a} = \sqrt{a}$

4) $\displaystyle \sqrt{49c}- \sqrt{16c}+ \sqrt{25c}= \sqrt{7^2c}- \sqrt{4^2c}+ \sqrt{5^2c}=$

$\displaystyle = 7 \sqrt{c}-4 \sqrt{c}+5 \sqrt{c}=8 \sqrt{c}$

5) $\displaystyle 2 \sqrt{18a}+0.5 \sqrt{72b}- \sqrt{98a}+ \sqrt{8b}=2 \sqrt{9*2*a}+0.5 \sqrt{36*2*b}-$
$\displaystyle - \sqrt{49*2*a}+ \sqrt{4*2*b}=6 \sqrt{2a}+3 \sqrt{2b}-7 \sqrt{2a}+2 \sqrt{2b}=$
$\displaystyle= 5 \sqrt{2b}- \sqrt{2a}$

6) $\displaystyle 5 \sqrt{2a}-0.4 \sqrt{125k}- \sqrt{32a}+ \sqrt{500k}=5 \sqrt{2a}-0.4 \sqrt{25*5k}-$
$\displaystyle - \sqrt{16*2*a}+ \sqrt{100*5*k}=5 \sqrt{2a}-2 \sqrt{5k}-4 \sqrt{2a}+10 \sqrt{2k}=$
$\displaystyle = \sqrt{2a}+8 \sqrt{5k}$

6) $\displaystyle \sqrt{75}- \frac{2}{7} \sqrt{147}+0.75 \sqrt{48}= \sqrt{25*3}- \frac{2}{7} \sqrt{49*3}+0.75 \sqrt{16*3}=$
$\displaystyle =5 \sqrt{3}-2 \sqrt{3}+3 \sqrt{3}=6 \sqrt{3}$

7) $\displaystyle \sqrt{275}-10 \sqrt{11}- \frac{2}{3} \sqrt{99}= \sqrt{25*11}-10 \sqrt{11}- \frac{2}{3} \sqrt{9*11}=$
$\displaystyle = 5 \sqrt{11}-10 \sqrt{11}-2 \sqrt{11}=-7 \sqrt{11}$