Question

please explain not just give answer

What is the exact value of the expression 2the square root of 7. + the square root 14. + 4the square root of 7.?

4 the square root of 7. + the square root of 14.
6 the square root of 7. + the square root 14.
7 the square root of 28.
the square root of 28.

Answer 1

let x be the square root of 7
let y be the square root of 14

\[\Large 2\sqrt{7} + \sqrt{14} + 4\sqrt{7}\]

\[\Large 2x + y + 4x\]

Answer 2

simplify 2x+y+4x and then substitute the root values back in

Answer 3

For the common roots , addition can look like this
\[a \sqrt{b} + c \sqrt{b} = (a+c)\sqrt{b}\]

Answer 4

For unlike roots, you can not add
\[\sqrt{14}+\sqrt{7} = \sqrt{14}+\sqrt{7}\]

Answer 5

im lost...

Answer 6

If you have the same number under the root sign, you can add them together.
for example.
\[4\sqrt{5}+\sqrt{3 }+6\sqrt{5} = (4+6)\sqrt{5} + \sqrt{3} = 10\sqrt{5}+\sqrt{3}\]

Answer 7

Do you see how I replaced all the copies of "square root of 7" with x ?