Question

Simplify ( root3-root5) (root5+root3) ÷ 7-2 root5

Answer 1

Hi ,

[ (√3 - √5 )(√5 + √3)]/( 7 - 2√5 )

= [ ( √3 )² - ( √5 )² ( 7 + 2√5 )]/[(7-2√5)(7+2√5)]

= [ ( 3 - 5 )( 7 + 2√5 ) ]/[ 7² - ( 2√5 )² ]

= [ ( -2 ) ( 7 + 2√5 ) ] / [ 49 - 20 ]

= [ ( -2) (7 + 2√5 ) ]/29

I hope this helps you.

: )

Answer 2

Answer:

−0.7910

Step-by-step explanation:

Given : $\frac{(\sqrt{3} - \sqrt{5})(\sqrt{5} +\sqrt{3})}{7-2\sqrt{5}}$

To Find: Simplify

Solution:

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

$\sqrt{3}=1.732$

$\sqrt{5}=2.236$

Substitute the values

$\frac{(1.732 - 2.236)(2.236+1.732)}{7-2(2.236)}$

$\frac{(-0.504)(3.968)}{2.528}$

$-0.7910$

Hence  $\frac{(\sqrt{3} - \sqrt{5})(\sqrt{5} +\sqrt{3})}{7-2\sqrt{5}}=-0.7910$