Question

simplify 3 root 5 minus root 7 by 3 root 3 + root 2

Answer 1

I think this is the answer

Answer 2

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,

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

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

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

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

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

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

$=\frac{15.37}{25}$

$=0.6148$

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