Question

6 root 5 minus 5 root 3 upon 2 root 3 + 4 root 5 rationalize the denominator

Answer 1

Question:-

➜Rationalize:-

๛$\frac{6 \sqrt{5}-5 \sqrt{3}}{2 \sqrt{3}+4 \sqrt{5}}$

$\rule{200}{1}$

AnsWer:-

➜$\frac{6 \sqrt{5}-5 \sqrt{3}}{2 \sqrt{3}+4 \sqrt{5}}$

✪Multiply By 2√3-4√5✪

↝$\frac{(6 \sqrt{5}-5 \sqrt{3})(2 \sqrt{3}-4 \sqrt{5})}{(2 \sqrt{3}+4 \sqrt{5})(2 \sqrt{3}-4 \sqrt{5}}$

↝$\frac{(6 \sqrt{5}-5 \sqrt{3})(2 \sqrt{3}-4 \sqrt{5})}{(2 \sqrt{3})^{2}-(4 \sqrt{5})^{2}}$

↝$\frac{(6 \sqrt{5}-5 \sqrt{3})(2 \sqrt{3}-4 \sqrt{5})}{12-80}$

↝$\frac{(6 \sqrt{5}-5 \sqrt{3})(2 \sqrt{3}-4 \sqrt{5})}{-68}$

$\rule{200}{2}$

Answer 2

Step-by-step explanation:

(6√5 - 5√3 )/(2√3 +4√5)

(6√5 - 5√3 )/(2√3 +4√5) × (2√3-4√5)/(2√3-4√5)

(6√5 - 5√3 )×(2√3-4√5) / (2√3 +4√5)×(2√3-4√5)

(6√5 - 5√3 )×(2√3-4√5)/{ (2√3)^2 - (4√5)^2 }

(6√5 - 5√3 )×(2√3-4√5)/( 12 - 80 )

(6√5 - 5√3 )×(2√3-4√5)/ (-68)

✓✓✓