Chapter 7.5, Problem 51PPE

To determine

To simplify: the given expression by converting into radical expression.

Answer to Problem 51PPE

  $7\sqrt{x^3}\text{ or }7x^{\frac{3}{2}}$

Explanation of Solution

Given information: an expression is given as follows-

  $4x^{\frac{3}{2}}+3\sqrt{x^3}$

We can write $4x^{\frac{3}{2}}$ as follows

  $4x^{\frac{3}{2}}=4{(x^3)}^{\frac{1}{2}}=4\sqrt{x^3}$

Now the given expression is $4x^{\frac{3}{2}}+3\sqrt{x^3}$= $4\sqrt{x^3}+3\sqrt{x^3}=7\sqrt{x^3}$

Yes, we can add the resulting terms.

The result in simplest form is $7\sqrt{x^3}$ .

Yes we can write the results into two equivalent forms,

And the two equivalent forms are $7\sqrt{x^3}$ and $7x^{\frac{3}{2}}$ .