Question

Evaluate the square root of -4 times the square root of -25 and the square root of 100. Does the rule square root of a times the square root of b = square root of ab hold when a and b are negative numbers.

Answer 1

\(\bf \sqrt{-4}\cdot \sqrt{-25}\cdot \sqrt{100}?\)

Answer 2

so... do you undersand what " Does the rule square root of a times the square root of b = square root of ab hold when a and b are negative numbers. " means?

that is\(\bf \sqrt{a}\cdot \sqrt{b}\iff\sqrt{a\cdot b}\)

does that apply to negative radicands

Answer 3

that is, do you understand what you're asked?

Answer 4

yes

Answer 5

hm

Answer 6

ok

Answer 7

\(\bf \sqrt{-4}\cdot \sqrt{-25}\implies \sqrt{-4\cdot -25}\implies \sqrt{+100}\) is that true?

Answer 8

yea

Answer 9

well, I have disappointing news :|
is not

\(\bf \sqrt{-4}\cdot \sqrt{-25}\implies\sqrt{-1\cdot 4}\cdot \sqrt{-1\cdot 25}
\\ \quad \\
\sqrt{-1}\cdot \sqrt{4}\cdot \sqrt{-1}\cdot \sqrt{25}\implies 2i\cdot 5i\implies 10{\color{brown}{ i^2}}\implies 10({\color{brown}{ -1}})\implies -10\)

Answer 10

ok

Answer 11

that rule, does not apply to negative radicands, when the root is EVEN
you first, take out the imaginary part, that is \(\bf \sqrt{-1}\) and then simplify

Answer 12

ok thanks i understand it now

Answer 13

yw