Question

How can I simplify this..
45^(1/2) -5

Answer 1

remember
\[x^{1/2}=\sqrt{x}\]
so
\[45^{1/2}=\sqrt{45}\]

Answer 2

Yeah I know that. But how to solve..

Answer 3

Are there any easy square numbers that are factors of 45?

Answer 4

\[\sqrt{45}\] = \[\sqrt{9\times5} = \sqrt{3^{2}\times5} = 3\sqrt{5}\]
what do you mean like this?

Answer 5

\[3\sqrt{5}-5= what\]

Answer 6

That's all.. you are just simplifying

Answer 7

Can't we simplify further

Answer 8

It is similar to simplifying fractions... at the end, you just have a more simple expression than you started with

Answer 9

Yeah I agree with u all

Answer 10

how about this
\[3\sqrt{5}-5=x\]

Answer 11

What do you mean? Are you asking whether you can express your response like that? Or are you asking whether you can simplify further?

Answer 12

Can\[(3\sqrt{5}-5)^{2}=x ^{2}\]'t we remove the root by squaring both sides

Answer 13

by squaring both sides, you have two terms inside the parenthesis. You can't just apply the "square" to the first term to remove the root, because that expression is really:\[(3\sqrt{5} - 5)(3\sqrt{5}-5) = (3\sqrt{5})^{2}-2(5)(3\sqrt{5)}) +\]

Answer 14

oops, left off the 25 off the end of that

Answer 15

It all simplifies down the same anyway, except with other unintended problems that don't matter for this one.

Your earlier answer may not look "done", but it was really correct... completely simplified

Answer 16

Ohh thank U very much for your respond

Answer 17

Squaring both sides for something like this is probably a bad instinct... @completeidiot might be able to tell you why

Answer 18

ug what a mess this has become
we started with this
\[45^{1/2} -5= \sqrt{45}-5\]

all you really need to do is simplify the square root
getting
\[3\sqrt5-5\]

this is your simplified expression

it doesnt need to be equal to anything
remember that an expression is not the same as an equation

Answer 19

an expression is very different from an equation

if you're asked to simplify an expression, the result will still be an expression

remember that an equation has an equal sign in it

why squaring both sides is a bad idea with that equation
simple answer, you still get sqrt(5) on one side which doesnt really help

and if x=35√−5
why would you need to do anything further if you already know x

Answer 20

long story short
expressions dont need to be equal to anything

Answer 21

Yeah I agree with u I didn't know abt the difference between an expression an an equation thnx for explaining abt this Thnx very much I really appreciate both of u @completeidiot & @JakeV8 V8

Answer 22

\[\sqrt{45}=3\sqrt{5}=6.7082 is simplfied answer i think this on minus with f gives u 1.7082

Answer 23

Unless they are asking you to run it through a calculator, typically you can leave it in a simplified form that includes a root. If you need the decimals, by all means, use the calculator, but it's just two different forms.