Question

What is a3b4−−−−√ expressed in simplified form?

a2bb√

ab2a√

ab2ab−−√

abab−−√

Answer 1

`ab^2√(a)`

Explanation:

We are asked to express
`√(a^3b^4)` in simplified form.

Using radical rule
`√(mn)=√(m)\cdot √(n)`, we will get:

`√(a^3b^4)=√(a^3)\cdot√(b^4)`

Rewrite
`a^3` as
`a^2\cdot a` and
`b^4` as
`(b^2)^2`

`√(a^3b^4)=√(a^2\cdot a)\cdot√((b^2)^2)`

Using radical rule
`√(mn)=√(m)\cdot √(n)`, we will get:

`√(a^3b^4)=√(a^2)\cdot√(a)\cdot√((b^2)^2)`

Using radical rule
`\sqrt[n]{m^n}=m`,we will get:

`√(a^3b^4)=a\cdot b^2\cdot√(a)`

`√(a^3b^4)=ab^2\cdot√(a)`

Therefore, the simplified form of the given expression would be
`ab^2√(a)`.