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+√500k6)√75-√147+0,75√487)√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)  $\displaystyle \sqrt{275}-10 \sqrt{11}- \frac{2}{3} \sqrt{99}= \sqrt{25*11}-10 \sqrt{11}- \frac{2}{3} \sqrt{9*11}=$
$\displaystyle = 5 \sqrt{11}-10 \sqrt{11}-2 \sqrt{11}=-7 \sqrt{11}$

Answer 2

1. a√x + b√x - m√x - b√x = (a-m)√x

2. 2√a + 3√a - 4√a = √a

3. √49с - √16с + √25с = 7√c - 4√c + 5√c = 8√c

4. 2√18a - √98a + 0.5√72b + √8b = (2√9a - √49a) + (0.5√36b + √4b) - √98a = 3√a + √40b - √98a = (3-√98)a + √40b

5. 5√2a - √32a - 0.4√125k + √500k = (5√2a - √32a) - (0.4√25k - √100k) = (5√2 - 4)√a + (2√125 - 10√5)√k = (5√2 - 4)√a + 10√5√k

6. √75 - √147 + 0.75√48 = 5√3 - 7√3 + 6√2 = -2√3 + 6√2

7. √275 - 10√11 - √99 = 5√11 - 10√11 - 3√11 = -8√11