Question

Can someone help! I know the answer I just need step by step!

Answer 1

4
`√(2)`

Explanation:

using the rule of radicals

`√(a)` ×
`√(b)` ⇔
`√(ab)`

`√(32)`

=
`√(16(2))`

=
`√(16)` ×
`√(2)`

= 4
`√(2)`

Answer 2

`4 √(2)`

Explanation:

Rewrite 32 as the product of 16 and 2:

`\implies √(32)=\sqrt{16 \cdot 2`

Apply exponent rule
`√(a \cdot b)=√(a)√(b)`

`\implies √(16 \cdot 2)=√(16)√(2)`

Rewrite 16 as 4²:

`\implies √(16)√(2)=√(4^2)√(2)`

Apply exponent rule
`√(a^2)=a`

`\implies √(4^2)√(2)=4 √(2)`