Question

Double check my work? I have to find the simplified expression and think I got the wrong answer. I will put the equation in the comments

Answer 1

\[5\sqrt{v^8} -\sqrt{v^3} - \sqrt{16v^8} + 3\sqrt{v^3}\]

Answer 2

\[v^8=(v^2)^4\]\[v^3=v^{2+1}\]\[brake~~~~the~~~~the~~~~roots.\]

Answer 3

Any ideas?

Answer 4

Keep in mind a couple things:
\[\sqrt{ab} = \sqrt{a}\sqrt{b}\]

In this case, \(\sqrt{16v^8} = \sqrt{16}\sqrt{v^8}\)

Also, pair the terms in this manner:
\[5\sqrt{v^8} - \sqrt{16v^8} + 3\sqrt{v^3}-\sqrt{v^3}\]

Answer 5

Remember:
\(\sqrt{16} = 4\)
\(\sqrt{(x^a)^2} = x^a\)

Answer 6

In this case:

\(\sqrt{v^8} = \sqrt{(v^4)^2} = v^4\)

Answer 7

That might seem like a lot to absorb at once. There's one last thing I want to mention.

Answer 8

Distributive Property:

\(ab + ac = a(b + c)\)

You may be wondering how distributive property is relevant to this.

Answer 9

Well...notice that \(\sqrt{v^8}\) is common to two terms and \(\sqrt{v^3}\) is common to two terms.

Answer 10

We can factor those out using distributive property. But first we should reduce the expressions in accordance with the aforementioned rules.

Answer 11

\(5\sqrt{v^8} - \sqrt{16v^8} + 3\sqrt{v^3}-\sqrt{v^3}\) becomes:
\(5\sqrt{v^8} - 4\sqrt{v^8} + 3\sqrt{v^3}-\sqrt{v^3}\) by square root property
\((5 - 4)\sqrt{v^8} + (3 - 1)\sqrt{v^3}\) by distributive property
\((1)\sqrt{v^8} + (2)\sqrt{v^3}\) by simplification

Answer 12

The only thing left to reduce is \(\sqrt{v^8}\) We already know from above that it simplifies to \(v^4\) so the final simplified resullt is:
\(v^4 + 2\sqrt{v^3}\)