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9. Express in simplest radical form with a rational denominator.

9. Express in simplest radical form with a rational denominator.-example-1
User EugenSunic
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1 Answer

2 votes

The given rational fraction is


(√(49x^8))/(√(7x^3))

We will simplify it

First, simplify the numerator

Find the square root of 49 and the square root of x^8


\begin{gathered} √(49)=7 \\ √(x^8)=x^{(8)/(2)}=x^4 \\ √(49x^8)=7x^4 \end{gathered}

Now, simplify the denominator

Find the square root of x^3


\begin{gathered} x^3=x* x* x \\ √(x^3)=√(x^2* x)=x√(x) \\ √(7x^3)=x√(7x) \end{gathered}

The fraction is


(7x^4)/(x√(7x))

Simplify x^4 up with x down by subtracting their powers


(7x^(4-1))/(√(7x))=(7x^3)/(√(7x))

Multiply up and down by root 7x to rationalize the denominator


\begin{gathered} (7x^3)/(√(7x))*(√(7x))/(√(7x))= \\ \\ (7x^3(√(7x)))/(7x)= \end{gathered}

Simplify 7x^3 up with 7x down


(7x^3)/(7x)=(7)/(7)x^(3-1)=1(x^2)=x^2

Then the simplest form is


x^2√(7x)

The answer is


x^2√(7x)

User Arkajit
by
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