I am trying to multiply and simplify the following radical expression.

$$(\sqrt{x}+5 - 4)(\sqrt{x}+5+4)$$

According to the book, the answer is $x - 11$

However, I am confused about how this even works. I tried using the following calculator that shows all the steps. http://www.softmath.com/math-com-calculator/adding-matrices/multiply-radical-expressions.html#c=simplify_algstepssimplify&v217=%2528%25u221Ax%2B5%2520-%25204%2529%2528%2520%25u221Ax%2B5%2B4%2529

However, the answer is completely different when using the calculator $x + 10\sqrt{x} + 9$.

I know I must be missing something here and it is probably something simple. I can simplify radicals by themselves with no problem, but when they are multiplied that is when I get into trouble.

  • 7
    $\begingroup$ The book's answer corresponds to this product $$\left(\sqrt{x+5}-4\right)\left(\sqrt{x+5}+4\right)$$ but you entered $$\left(\sqrt{x}+5-4\right)\left(\sqrt{x}+5+4\right)$$ into the calculator. See the difference? $\endgroup$ – Blue Feb 17 at 15:11
  • $\begingroup$ Thanks, I knew I was missing something simple. $\endgroup$ – Curt Rand Feb 17 at 15:17

You have: $$(\sqrt{x+5}-4)(\sqrt{x+5}+4)$$ Your lack of collecting the $+5$ under the square root is why your calculator procured the incorrect answer.

Instead, use Difference of Two Squares here: $$(A-B)(A+B)=A^2-B^2$$ (achievable by expanding)

  • $\begingroup$ I knew I was missing something stupidly simple. Thank you for your help. $\endgroup$ – Curt Rand Feb 17 at 15:17
  • $\begingroup$ No problem. Always have to be careful when displaying math in calculators. $\endgroup$ – Rhys Hughes Feb 17 at 15:21

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.