Question

Simplify :- 28/ root28-root7

Answer 1

Step-by-step explanation:

Given

$\frac{28}{ \sqrt{28} - \sqrt{7 } } \\ = \frac{28}{2 \sqrt{7} - \sqrt{7} } \\ = \frac{28}{(2 - 1) \sqrt{7} } \\ = \frac{28}{ \sqrt{7} }$

Ans = 28/7^1/2

Answer 2

Answer:

$\frac{4(\sqrt{28} + \sqrt{7} )}{3}$ is the required value of $\frac{28}{\sqrt{28} - \sqrt{7} }$

Step-by-step explanation:

Explanation:

Given that, $\frac{28}{\sqrt{28} - \sqrt{7} }$

• Rationalization - An irrational number is rationalised, or changed into a number that can be stated as the ratio of two integers, through the process of rationalisation.

• For this question we rationalization the denominator than we simplify it.

Step 1:

From the question we have,  $\frac{28}{\sqrt{28} - \sqrt{7} }$

On multiplying both denominator and numerator by

$\frac{28}{\sqrt{28} - \sqrt{7} }$ × $\frac{\sqrt{28} + \sqrt{7} }{\sqrt{28} + \sqrt{7} }$ = $\frac{28(\sqrt{28} + \sqrt{7} )}{(\sqrt{28} )^2 - (\sqrt{7})^2 }$

As we know that the formula, $a^2 - b^2 = (a +b)(a -b)$

⇒$\frac{28(\sqrt{28} + \sqrt{7} )}{28 - 7}$ = $\frac{28(\sqrt{28} + \sqrt{7} )}{21}$ = $\frac{4(\sqrt{28} + \sqrt{7} )}{3}$

Final answer:

Hence, $\frac{4(\sqrt{28} + \sqrt{7} )}{3}$ is the required value of $\frac{28}{\sqrt{28} - \sqrt{7} }$.

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