Math help please?

Question

Can you simplify this problem for me please.

Va7 * b3 * c5

V= square root sign

* = multiplying sign

Answer 1

The square root is equivalent to dividing the exponent by two. So, for example, sqrt(a^6) = a^3.

This means that you can move any even-numbered power out of the square root, dividing the exponent by two in the process.

Since the exponent on a, b, and c are all odd, there's a single factor of a, b, and c left behind:

a^3 * b * c^2 * sqrt(abc)

It can be done in more steps:

sqrt( a^7 * b^3 * c^5 ) =
sqrt( a^6 * a * b^2 * b * c^4 * c ) =
sqrt(a^6) * sqrt(b^2) * sqrt(c^4) * sqrt(abc) =
a^3 * b * c^2 * sqrt(abc)

You could also write it out as:

a^(7/2) * b^(3/2) * c^(5/2)

... but usually in these sorts of problems you're supposed to use the square root symbol instead of using a non-integer exponent.

Answer 2

I'm going to use rt( ) to signify square root. Also, I'm going to assume that all three factors are underneath the square root.

What you would do is try to find as many terms that can be simplified out of the square root sign. For example, rt(a^2) can be simplified to a. rt(a^3) = a*rt(a).

rt(a^7 * b^3 * c^5)
= rt (a^6 *a * b^2*b * c^4*c)
= a^3 * b * c^2 *rt(abc)

Answer 3

If all parts are under the radical sign then =
a^3.5 * b^1.5 * c^2.5

If it's only a^7 under the radical sign then a^3.5 * b^3 * c^5.