Question

Упростите
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-$frac{2}{7}$√147+0,75√48
7)√275-10√11-$frac{2}{3}$√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) $displaystyle sqrt{275}-10 sqrt{11}- frac{2}{3} sqrt{99}= sqrt{25*11}-10 sqrt{11}- frac{2}{3} sqrt{9*11}=$
$displaystyle = 5 sqrt{11}-10 sqrt{11}-2 sqrt{11}=-7 sqrt{11}$