Question

Simplifying rational expressions.

Simplify (2√5+3√7)^2

Simplify 4√6/√30 by rationalizing the denominator.

Answer 1

\[(2\sqrt5+3\sqrt7)(2\sqrt5+3\sqrt7)\] is a start

Answer 2

for the second one start with
\[\frac{4}{\sqrt{5}}\] and then multiply by 1 in the form of
\[\frac{4}{\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}\]

Answer 3

@satellite73 is the answer for the second one 4√5/5

Answer 4

yes

Answer 5

ok i really dont know the first one though can you explain a little more?

Answer 6

you have to multiply out using the distributive property
\[(a+b)^2=(a+b)(a+b)=a^2+2ab+b^2\] or in this case it would be easier to compute at
\[(a+b)^2=a^2+b^2+2ab\]

Answer 7

\[(2\sqrt5+3\sqrt7)(2\sqrt5+3\sqrt7)\]
\[=(2\sqrt{2})^2+(3\sqrt{7})^2+2\times 2\sqrt{5}\times 3\sqrt{7}\] is the first step

Answer 8

oops typo there, should be
\[=(2\sqrt{5})^2+(3\sqrt{7})^2+2\times 2\sqrt{5}\times 3\sqrt{7}\]

Answer 9

then
\[4\times 5+9\times 7+12\sqrt{5\times 7}\]

Answer 10

i will let you finish it from there

Answer 11

95√35 i think

Answer 12

no

Answer 13

If that's not it idk the answer.