Question

Sqrt of 4a-4 + sqrt of a-1

Answer 1

$\large\begin{array}{l} \textsf{Simplify the expression (I'm goint to call it E)}\\\\ \mathsf{E=\sqrt{4a-4}+\sqrt{a-1}} \end{array}$


$\large\begin{array}{l} \textsf{So E is a sum of two square roots. Notice that you can factor}\\\textsf{the 4 out on the first one:}\\\\ \mathsf{E=\sqrt{4\cdot a-4\cdot 1}+\sqrt{a-1}}\\\\ \mathsf{E=\sqrt{4\cdot (a-1)}+\sqrt{a-1}}\\\\ \mathsf{E=\sqrt{2^2\cdot (a-1)}+\sqrt{a-1}}\\\\ \mathsf{E=\sqrt{2^2}\cdot \sqrt{a-1}+\sqrt{a-1}}\\\\ \mathsf{E=2\cdot \sqrt{a-1}+\sqrt{a-1}} \end{array}$

$\large\begin{array}{l} \mathsf{E=2\cdot \sqrt{a-1}+1\cdot \sqrt{a-1}}\\\\ \mathsf{E=(2+1)\cdot \sqrt{a-1}}\\\\ \boxed{\begin{array}{l}\mathsf{E=3\cdot \sqrt{a-1}} \end{array}} \end{array}$


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$\large\textsf{I hope this helps. :-)}$


Tags: square root sqrt simplify expression radical irrational algebra