Question

Simplify:
-5(sqaure root symbol)112

Answer 1

\[-5\sqrt{112}\]

Answer 2

\(\bf -5\sqrt{112}
\\ \quad \\
{\color{brown}{ 112\to 2\cdot 2\cdot 2\cdot 2\cdot 7\to 2^2\cdot 2^2\cdot 7\to (2^2)^2\cdot 7}}\qquad thus
\\ \quad \\
-5\sqrt{112}\implies -5\sqrt{(2^2)^2\cdot 7}\implies -5\sqrt{(2^2)^2}\cdot \sqrt{7}\implies ?\)

Answer 3

how do i solve that

Answer 4

well... what's \(\Large \sqrt[{\color{red}{ 2}}]{x^{\color{red}{ 2}}}\implies ?\)

Answer 5

Use a factor tree, go on khan acdemy, im sure its there :P

Answer 6

i know how to do a factor tree i just get confused after that

Answer 7

so.... when taking roots..... what \(\Large \sqrt[{\color{red}{ 2}}]{x^{\color{red}{ 2}}}\implies ?\) would be? notice, the radicand exponent "matches" the root

Answer 8

so itd be 16?

Answer 9

well \(\bf (2^2)^2\) is 16 yes.. but once "out of the radical" is not