Question

Need help with these question give me tha answer

Answer 1

Part 1)
`2√(6)`

Part 2)
`4√(5)`

Part 3)
`36√(10)`

Part 4)
`15√(5)`

Part 5)
`20√(5)`

Part 6)
`9√(2)`

Explanation:

Part 1) we have

`√(24)`

we know that

`24=(2^(3))(3)`

Remember that

`\sqrt{a^(2)}=a`

substitute

`\sqrt{(2^(3))(3)}=\sqrt{(2^(2))(2)(3)}=2√(6)`

Part 2) we have

`√(80)`

we know that

`80=(2^(4))(5)`

Remember that

`\sqrt{a^(2)}=a`

substitute

`\sqrt{(2^(4))(5)}`

we have that

`(2^(4))=(2^(2))^(2)=4^(2)`

substitute

`\sqrt{(4^(2)(5)}=4√(5)`

Part 3) we have

`12√(90)`

we know that

`90=(2)(3^(2))(5)`

Remember that

`\sqrt{a^(2)}=a`

substitute

`12\sqrt{(2)(3^(2))(5)}=12\sqrt{(3^(2))(5)(2)}=(12)(3)√((5)(2))=36√(10)`

Part 4) we have

`3√(125)`

we know that

`125=(5^(3))`

Remember that

`\sqrt{a^(2)}=a`

substitute

`3\sqrt{(5^(3))}=3\sqrt{(5^(2))(5)}=(3)(5)√(5)=15√(5)`

Part 5) we have

`2√(500)`

we know that

`500=(2^(2))(5^(3))`

Remember that

`\sqrt{a^(2)}=a`

substitute

`2\sqrt{(2^(2))(5^(3))}=2\sqrt{(2^(2))(5^(2))(5)}=(2)(2)(5)√(5)=20√(5)`

Part 6) we have

`√(162)`

we know that

`162=(2)(3^(4))`

Remember that

`\sqrt{a^(2)}=a`

substitute

`\sqrt{(2)(3^(4))}=\sqrt{(2)(3^(2))^(2)}=(3^(2))√((2))=9√(2)`