University of Kwazulu-Natal

Simplify Radical Expressions Combine Radicals Multiply And Studocu

Bonisiwe Shabane
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simplify radical expressions combine radicals multiply and studocu

How do we multiply radical expressions together? For example, consider It is tempting to just multiply the two numbers together, but is that correct? The key is to use what we learned in the previous section. Remember that since radicals are really equivalent to rational exponents, every exponent property gives us a corresponding radical property! First recall our Power of a Product rule for exponents, which works for any rational exponent [latex]m[/latex] as long as both [latex]a^m[/latex] and [latex]b^m[/latex] are real numbers:

Now, evaluate the above expression using an exponent of [latex]\dfrac{1}{2}[/latex] to represent the square roots: [latex]\begin{align} &\quad\sqrt{2}\cdot \sqrt{18} \\ =&\quad 2^{1/2}\cdot18^{1/2} \\ =&\quad(2\cdot18)^{1/2} && \color{blue}{\textsf{Power of a Product used here}}\\ =&\quad(36)^{1/2} \\ =&\quad \sqrt{36} \\ =&\quad 6 \end{align}[/latex] So we have shown that you can indeed multiply radicals by multiplying the radicands. It was crucial in our process that the exponents were equal to be able to use the Power of a Product rule. Thus radical multiplication only works this way if the indices are the same. In order to continue enjoying our site, we ask that you confirm your identity as a human.

Thank you very much for your cooperation. \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \) \( \newcommand{\dsum}{\displaystyle\sum\limits} \) \( \newcommand{\dint}{\displaystyle\int\limits} \) \( \newcommand{\dlim}{\displaystyle\lim\limits} \)

Answer: Use the rule [latex] \sqrt[x]{a}\cdot \sqrt[x]{b}=\sqrt[x]{ab}[/latex] to multiply the radicands. [latex]\begin{array}{r}\sqrt{18\cdot 16}\\\\\sqrt{288}\end{array}[/latex] [latex] \sqrt{{{(12)}^{2}}\cdot 2}[/latex] [latex] \sqrt{{{(12)}^{2}}}\cdot \sqrt{2}[/latex] [latex]\begin{array}{r}\left| 12 \right|\cdot \sqrt{2}\\12\cdot \sqrt{2}\end{array}[/latex] In the first section, we talked about the importance of simplifying radical expressions, and there's a reason for doing this that we didn't mention then: writing radical expressions in simplest form may allow us...

This expression can be simplified by first simplifying each individual term: When we simplify each of these, we obtain:

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How Do We Multiply Radical Expressions Together? For Example, Consider

How do we multiply radical expressions together? For example, consider It is tempting to just multiply the two numbers together, but is that correct? The key is to use what we learned in the previous section. Remember that since radicals are really equivalent to rational exponents, every exponent property gives us a corresponding radical property! First recall our Power of a Product rule for expon...

Now, Evaluate The Above Expression Using An Exponent Of [latex]\dfrac{1}{2}[/latex]

Now, evaluate the above expression using an exponent of [latex]\dfrac{1}{2}[/latex] to represent the square roots: [latex]\begin{align} &\quad\sqrt{2}\cdot \sqrt{18} \\ =&\quad 2^{1/2}\cdot18^{1/2} \\ =&\quad(2\cdot18)^{1/2} && \color{blue}{\textsf{Power of a Product used here}}\\ =&\quad(36)^{1/2} \\ =&\quad \sqrt{36} \\ =&\quad 6 \end{align}[/latex] So we have shown that you can indeed multiply ...

Thank You Very Much For Your Cooperation. \( \newcommand{\vecs}[1]{\overset {

Thank you very much for your cooperation. \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \) \( \newcommand{\dsum}{\displaystyle\sum\limits} \) \( \newcommand{\dint}{\displaystyle\int\limits} \) \( \newcommand{\dlim}{\displaystyle\lim\limits} \)

Answer: Use The Rule [latex] \sqrt[x]{a}\cdot \sqrt[x]{b}=\sqrt[x]{ab}[/latex] To Multiply The

Answer: Use the rule [latex] \sqrt[x]{a}\cdot \sqrt[x]{b}=\sqrt[x]{ab}[/latex] to multiply the radicands. [latex]\begin{array}{r}\sqrt{18\cdot 16}\\\\\sqrt{288}\end{array}[/latex] [latex] \sqrt{{{(12)}^{2}}\cdot 2}[/latex] [latex] \sqrt{{{(12)}^{2}}}\cdot \sqrt{2}[/latex] [latex]\begin{array}{r}\left| 12 \right|\cdot \sqrt{2}\\12\cdot \sqrt{2}\end{array}[/latex] In the first section, we talked abo...

This Expression Can Be Simplified By First Simplifying Each Individual

This expression can be simplified by first simplifying each individual term: When we simplify each of these, we obtain: