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$\sqrt{7-\sqrt{13}}\times\sqrt{7+\sqrt{13}}$

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Multiply radical expressions

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Q.

\sqrt{7-\sqrt{13}}\times\sqrt{7+\sqrt{13}}

Apply difference of squares: Step $1$ : Apply the difference of squares formula, which states $(a - b)(a + b) = a^2 - b^2$ . $\newline$ Calculation: $(\sqrt{7-\sqrt{13}} \times \sqrt{7+\sqrt{13}}) = \sqrt{(7-\sqrt{13}) \times (7+\sqrt{13})} = \sqrt{7^2 - (\sqrt{13})^2}$
Simplify inside square root: Step $2$ : Simplify inside the square root. $\newline$ Calculation: $\sqrt{49 - 13} = \sqrt{36}$
Take square root: Step $3$ : Take the square root of $36$ . $\newline$ Calculation: $\sqrt{36} = 6$

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