simple one

[shell isle]

simple one but i can't get the answer :(((

[mossy canyon]

if?

[granite knot]

i suppose it asks us to simplify the expression @mossy canyon

[mossy canyon]

oh ok

[shell isle]

yeah

[granite knot]

except i cant understand the expression

is that 712 * sqrt(6)?

[shell isle]

yep

[granite knot]

not smth like 7 + 2 * sqrt(6)?

[shell isle]

712√6

[granite knot]

weird

[shell isle]

oh

wait lemme recheck

wait no u're right lmao

7+2√6

[granite knot]

hmm

[shell isle]

can you get it?

[granite knot]

trying to

also, like

[shell isle]

oh

[granite knot]

$x = \sqrt{\sqrt{6} + 6 + (\sqrt{7 + 2\sqrt{6}})} - \sqrt{6}$, right?

[grim cove]

John Math

[granite knot]

wait

yeah, like this?

[shell isle]

yeah yeah

[granite knot]

are you sure? please double check

[shell isle]

lmao ok brb

yeah

thats correct

[granite knot]

right so

[stiff egret]

I like your handwriting

[shell isle]

thats not even mine 💀💀

[granite knot]

if im correct, the answer should be 1

[shell isle]

thats my friend's

[shell isle]

is there like

procedurs

the steps

[granite knot]

there are methods that can be used to simplify the expression

so

[shell isle]

whats the easisty

easiest

can the bot show it for me

[granite knot]

observe

[shell isle]

observing

[granite knot]

we have this expression here

$x = \sqrt{\sqrt{6} + 6 + (\sqrt{7 + 2\sqrt{6}})} - \sqrt{6}$

[grim cove]

John Math

[granite knot]

we can simplify the

$\sqrt{7 + 2\sqrt{6}}$ part

[grim cove]

John Math

[shell isle]

okay

[granite knot]

we know that 7 = 6 + 1

[shell isle]

yeah

[granite knot]

so it can be rewritten as

$\sqrt{6 + 2\sqrt{6} + 1}$

[grim cove]

John Math

[granite knot]

noticed anything?

[shell isle]

yeah

break down 6 to √6

and take out the commons

and what.

[granite knot]

$\sqrt{\sqrt{6}^2 + 2\cdot 1\cdot\sqrt{6} + 1^2}$

[grim cove]

John Math

[shell isle]

yeah

oh wait

[granite knot]

we notice that it is equal to $(\sqrt{6}+1)^2$

[grim cove]

John Math

[shell isle]

OHHH

yeah yesh

[granite knot]

so we get

$\sqrt{(\sqrt{6}+1)^2}$

[grim cove]

John Math

[granite knot]

which is obviously just $\sqrt{6} + 1$

[grim cove]

John Math

[granite knot]

now back to our expression

[shell isle]

yeah

[granite knot]

$x = \sqrt{\sqrt{6} + 6 + (\sqrt{7 + 2\sqrt{6}})} - \sqrt{6}$

[grim cove]

John Math

[granite knot]

we went from this to this

$x = \sqrt{\sqrt{6} + 6 + (\sqrt{6} + 1)} - \sqrt{6}$

[grim cove]

John Math

[granite knot]

so far so good?

[shell isle]

yeah

mhm

[granite knot]

so now lets group terms and see what we can do here

$x = \sqrt{6 + 2\sqrt{6} + 1} - \sqrt{6}$

[grim cove]

John Math

[granite knot]

familiar, isnt it?

[shell isle]

yeah

looks like uh

yeah

the one we did earlier

[shell isle]

here

[granite knot]

so we get

$x = \sqrt{6} + 1 - \sqrt{6}$

[grim cove]

John Math

[granite knot]

and square roots cancel out

[shell isle]

damn

[granite knot]

we're left with x = 1

[shell isle]

thank you so much

🫶🫶🫶