quick question regarding this problem and why you halve the radicand

[amber radish]

what’s the question again ?

I didn’t get it

why the equality is right?

[nocturne wing]

No I know the equality is right I’m asking the reasoning for halving the 32 in the 1st step

Or the “law” behind the method of simplification

[muted pawn]

it's called factoring

[slim zodiac]

Well basically you have a long multiplication. So you factor out the 2 from the 32. You do this, because you can take the square root of 16, but not from 32 (or ar least not without a calculator.)

[nocturne wing]

thank you

this is what i didn't understand

i couldn't understand why 32 was any different than using 16

[slim zodiac]

Yeah. Its just so you can take the square root

[nocturne wing]

well yea

but i was just saying the sqrt of 16/32 is one in the same

[slim zodiac]

Or in this case even the fourth root

[nocturne wing]

and i didnt understand the difference for usage really

[slim zodiac]

Yeah. So you have\
$\sqrt[4]{32} = \sqrt[4]{2 \cdot 16} $\
$=\sqrt[4]{2} \cdot \sqrt[4]{16} = \sqrt[4]{2} \cdot 2$\

[uncut frost]

Valle

[nocturne wing]

.close