Question

Giving medals!!!!!!


Simplify.square root of 10 times square root of 8

square root of 18

4 square root of 5

square root of 80

None of the above

Answer 1

hint: \(\bf \sqrt{x}\cdot \sqrt{y}\implies \sqrt{x\cdot y}\)

Answer 2

same root, the radicands multiply each other

Answer 3

so I multiply 10 and 8 ?

Answer 4

well.... keeping the radical,yes
what did you get?

Answer 5

square root of 80

Answer 6

ok so \(\large {
\sqrt{10}\cdot \sqrt{8}\implies \sqrt{80}
\\ \quad \\
{\color{brown}{ 80\to 2\cdot 2\cdot 2\cdot 2\cdot 5\to 2^2\cdot 2^2\cdot 5\to (2^2)^2\cdot 5}}
\\ \quad \\
\sqrt{80}\implies \sqrt[{\color{blue}{ 2}}]{(2^2)^{\color{blue}{ 2}}\cdot 5}\implies ?
}\)

Answer 7

I'm not sure but, I thought it would be neither of them because I thought your not supposed to add the square roots.

Answer 8

hmm we didn't add any of the roots

Answer 9

multiply sorry

Answer 10

you can, IF the root is the same
in this case both are root 2, or square root, so they're both the same,
thus they're multiplyable

if the root were different, say \(\Large \sqrt[3]{10}\cdot \sqrt[5]{8}\)
then we couldn't

Answer 11

so \(\large {
\sqrt{10}\cdot \sqrt{8}\implies \sqrt{80}
\\ \quad \\
{\color{brown}{ 80\to 2\cdot 2\cdot 2\cdot 2\cdot 5\to 2^2\cdot 2^2\cdot 5\to (2^2)^2\cdot 5}}
\\ \quad \\
\sqrt{80}\implies \sqrt[{\color{blue}{ 2}}]{(2^2)^{\color{blue}{ 2}}\cdot 5}\implies ?
}\)

what do you think?

Answer 12

I'm not entirely sure about how to do this, so it's not the square root of 80 right?

Answer 13

well... yes it's notice the 1st line
but notice the red lines

is 2 * 2 * 2 * 2 * 5 \(\ne\ 80?\)