Question

Operations with Radical Expressions
Simplify 7√7 - 2√7



Please explain all the steps, I have these for homework and I'm trying to understand how to solve them, thanks. =)

Answer 1

how would you simplify:

7x - 2x

Answer 2

the problem you stated is very similar to this

Answer 3

@LemonLeaf - do you understand?

Answer 4

$$\large
2\sqrt{x}+3\sqrt{x} \ \color{red}{\text{ if a=}\sqrt{x}}\implies 2a+3a = \boxed{\ ?}
$$

Answer 5

so It would be 5√7?

Answer 6

perfect! :)

Answer 7

but do you understand why?

Answer 8

not really

Answer 9

ok - let me try and explain...

Answer 10

I suppose it's like simplifying with variables, but the variable being replaced with a square root

Answer 11

think of \(\sqrt{7}\) as some number.

then \(7\sqrt{7}\) just means 7 times this number.

so you can just replace \(\sqrt{7}\) by some symbol to represent its value - lets use 'x'.

therefore \(7\sqrt{7}=7x\)

Answer 12

and yes, you statement is true - you can think of it in that way as well

Answer 13

once the root element, that is the root and its content RESEMBLE the same, you can treat them as any variable and just work with their coefficients

Answer 14

oh okay that's simple enough, thanks for your help :)

Answer 15

but you must be careful to replace like-with-like

e.g. you couldn't simplify: \(7\sqrt{7}-2\sqrt{5}\)

because \(\sqrt{7}\) and \(\sqrt{5}\) are two DIFFERENT quantities.

Answer 16

yw :)

Answer 17

could you help me with another one? it's a bit different than this one

Answer 18

sure - just post it as a new question on the left please (after closing this one)

Answer 19

if it were say \(\sqrt{2}\ and \ \sqrt{3} \) then that wouldn't work, but if you had \(\large \sqrt[5]{2} \ and \ \sqrt[5]{2}\), then they RESEMBLE each other, then you can