Question

which expression is the simplified form of 4sqrt(v) + 4sqrt(v^6) - sqrt(25v) - sqrt(9v^6)

Answer 1

\[4\sqrt{v} + 4\sqrt{v^6}-\sqrt{25v}-\sqrt{9v^6}\]
We can't simplify sqrt(v), but we can simplify sqrt(v^6). \[v^3*v^3=v^6\] \[\sqrt{v^6} = v^3\]and we know that 25 and 9 are just 5 squared and 3 squared respectively. And \[\sqrt{a*b}=\sqrt{a}*\sqrt{b}\] so we can do this:

\[4\sqrt{v} + 4\sqrt{v^6}-\sqrt{25v}-\sqrt{9v^6} = 4\sqrt{v}+4v^3-\sqrt{25}\sqrt{v}-\sqrt{9}\sqrt{v^6} \]
\[= 4\sqrt{v}+4v^3 -5\sqrt{v}-3v^3 = v^3-\sqrt{v}\]

Answer 2

Thanks!!

Answer 3

sqrt(32) - sqrt(50) + sqrt(128)

Answer 4

Break the numbers down into their prime factors, for example 32 = 2*2*2*2*2, so \[\sqrt{32} = \sqrt{(2*2)*(2*2)*2} = (2*2)\sqrt{2}=4\sqrt{2}\]

Answer 5

thank you so much!!!! :)