Question

Find the negative square root of 48

Answer 1

Any answer choices?

Answer 2

no

Answer 3

Hmm the one I got is -6.9

Answer 4

Ok do you know how you would get that without using a calclutor?

Answer 5

I do not

Answer 6

ok thanks

Answer 7

you could factor 48 into its prime factors
2*2*2*2 * 3
and look for "pairs"
there are two pairs of "2's". "pull each pair out of the radical, and put only one of each out front:
\[ \sqrt{2\cdot 2 \cdot 2 \cdot 2 \cdot 3}= 2\cdot 2 \sqrt{3} \]
simplify 2*2 to 4
and we want the negative square root, so make it negative
\[ -4 \sqrt{3} \]
notice what we get if we multiply it by itself
\[ -4 \sqrt{3} \cdot -4 \sqrt{3} = -4\cdot -4 \cdot \sqrt{3} \cdot \sqrt{3} \\
=16 \cdot 3 = 48
\]

Answer 8

ok thanks i think i understand now