The question given above will require a good understanding of surd operation in order to arrive at the best answer. Thus, the answer to the question is:
[tex]\frac{7\sqrt{14} }{\sqrt{7}} = 7\sqrt{2}[/tex]
To solve this problem, we shall simply rationalise the denominator. This can be obtained as illustrated below:
[tex]\frac{7\sqrt{14}}{\sqrt{7}}\\\\Rationalise\\\\\frac{7\sqrt{14}}{\sqrt{7}} * \frac{\sqrt{7} }{\sqrt{7}}\\\\\frac{7\sqrt{14*7}}{\sqrt{7*7}}\\\\\frac{7\sqrt{98}}{\sqrt{49}}\\\\\frac{7\sqrt{98}}{7}\\\\\sqrt{98}\\\\\sqrt{98} = \sqrt{49*2} \\\sqrt{98} = \sqrt{49} * \sqrt{2} \\\sqrt{98} = 7\sqrt{2} \\\\Thus, \\\\\frac{7\sqrt{14}}{\sqrt{7}} = 7\sqrt{2}[/tex]
Therefore, from the calculations made above, the solution to the question is 7√2
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