Question

Simplify root 3+root11/3 root 5+7 root3 by rationalizing the denominator

Answer 1

Answer:

\frac{3\sqrt{5}-\sqrt{7}}{3\sqrt{3}+\sqrt{2}}=0.6148

Step-by-step explanation:

Given : Expression \frac{3\sqrt{5}-\sqrt{7}}{3\sqrt{3}+\sqrt{2}}

To find : Simplify the expression?

Solution :

Expression \frac{3\sqrt{5}-\sqrt{7}}{3\sqrt{3}+\sqrt{2}}

Rationalize the denominator,

=\frac{3\sqrt{5}-\sqrt{7}}{3\sqrt{3}+\sqrt{2}}\times \frac{3\sqrt{3}-\sqrt{2}}{3\sqrt{3}-\sqrt{2}}

=\frac{(3\sqrt{5}-\sqrt{7})(3\sqrt{3}-\sqrt{2})}{(3\sqrt{3})^2-(\sqrt{2})^2}

=\frac{9\sqrt{15}-3\sqrt{10}-3\sqrt{21}+\sqrt{14}}{27-2}

=\frac{9\sqrt{15}-3\sqrt{10}-3\sqrt{21}+\sqrt{14}}{25}

=\frac{9(3.87)-3(3.16)-3(4.58)+3.74}{25}

=\frac{34.85-9.48-13.74+3.74}{25}

=\frac{15.37}{25}

=0.6148

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Answer 2

Answer:

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