What is the difference of 5[radical 7] and 3[radical 28]?

Aug 9, 2016

Answer:

$\sqrt{7}$

Explanation:

Assumption: The question is asking $| \textcolor{w h i t e}{\frac{.}{.}} 5 \sqrt{7} - 3 \sqrt{28} \textcolor{w h i t e}{\frac{.}{.}} |$

Note that the two vertical lines represent an 'absolute' value. This means that no matter if what is inside the | | the outcome is always positive

Note that $4 \times 7 = 28 \to {2}^{2} \times 7 = 28$

Write the question as: $5 \sqrt{7} - 3 \sqrt{{2}^{2} \times 7}$

Take the ${2}^{2}$ outside the square root

$| \textcolor{w h i t e}{\frac{.}{.}} 5 \sqrt{7} - \left(3 \times 2\right) \sqrt{7} \textcolor{w h i t e}{\frac{.}{.}} | \text{ " ->" } | \textcolor{w h i t e}{\frac{.}{.}} 5 \sqrt{7} - 6 \sqrt{7} \textcolor{w h i t e}{\frac{.}{.}} |$

$| \textcolor{w h i t e}{\frac{.}{.}} - \sqrt{7} \textcolor{w h i t e}{\frac{.}{.}} | = + \sqrt{7}$