Question

simplify 3root32 - 2root50 + 4root128 - 20root18​

Answer 1

Answer:

-24root2

convert roots to min base root and simplify

Answer 2

Answer:

$3\sqrt{32}-2\sqrt{50}+4\sqrt{128}-20\sqrt{18}$

$3\sqrt{32} = 3\sqrt{2*2*2*2*2} = 3*2*2\sqrt{2} =12\sqrt{2}$

$2\sqrt{50}=2\sqrt{5*5*2} =2*5\sqrt{2} =10\sqrt{2}$

$4\sqrt{128}=4*\sqrt{2*2*2*2*2*2*2} =4*2*2*2\sqrt{2} =32\sqrt{2}$

$20\sqrt{18}=20\sqrt{3*3*2} =20*3\sqrt{2}=60\sqrt{2}$

$12\sqrt{2}-10\sqrt{2}+32\sqrt{2}-60\sqrt{2}$

Taking $\sqrt{2}$ common

$\sqrt{2}(12-10+32-60)$

$\sqrt{2}(-26)$

$-26\sqrt{2}$