Question

please refer to the picture and answer and also send a picture of your answer because its easy to understand thats why ​

Answer 1

$\large \sf {\red {\frac{ \sqrt{ 5 } + \sqrt{ 3 } }{ \sqrt{ 80 } + \sqrt{ 48 } - \sqrt{ 45 } - \sqrt{ 27 } }}}$

• Factor $80=4^{2}\times 5$.Rewrite the square root of the product $\sqrt{4^{2}\times 5}$as the product of square roots $\sqrt{4^{2}}\sqrt{5}.$ Take the square root of $4^{2}.$

$\:$

$\sf \: \frac{\sqrt{5}+\sqrt{3}}{4\sqrt{5} + \sqrt{48}-\sqrt{45}-\sqrt{27}}$

• Factor $48=4^{2}\times 3.$Rewrite the square root of the product $\sqrt{4^{2}\times 3}$as the product of square roots $\sqrt{4^{2}}\sqrt{3}.$Take the square root of $4^{2}.$

$\:$

$\sf \: \frac{\sqrt{5}+\sqrt{3}}{4\sqrt{5}+4\sqrt{3}-\sqrt{45}-\sqrt{27}}$

• Factor $45=3^{2}\times 5.$Rewrite the square root of the product $\sqrt{3^{2}\times 5}$as the product of square roots $\sqrt{3^{2}}\sqrt{5}.$ Take the square root of 3^{2}.

$\:$

$\sf \: \frac{\sqrt{5}+\sqrt{3}}{4\sqrt{5}+4\sqrt{3}-3\sqrt{5}-\sqrt{27}}$

$\:$

$\sf \: \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+4\sqrt{3}-\sqrt{27}}$

• Factor $27=3^{2}\times 3.$. Rewrite the square root of the product $\sqrt{3^{2}\times 3}$as the product of square roots $\sqrt{3^{2}}\sqrt{3}.$Take the square root of $3^{2}.$

$\:$

$\sf \: \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+4\sqrt{3}-3\sqrt{3}}$

$\:$

$\sf \: \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}$

$\:$

$1$

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