Question

Simplify. Remove all perfect squares from inside the square root. 30b^5

Answer 1

I am assuming that 30b⁵ is written under root since it is mention that remove all perfect squares from inside the square root.

$\sf \: \sqrt{30b ^{5} }$

Rewrite the exponent as a sum where one of the addends is a multiple of the index

$\sf \sqrt{30 {b}^{4 + 1} }$

Use $a ^{m + n} = {a}^{m} \times {a}^{n}$ To expand the expression

$\sf \sqrt{30b^{4} \times b ^{1} }$

Any expression raised to the power of 1 equals itself

$\sf \sqrt{30 {b}^{4} \times b}$

The root of a product is equal to the product of the roots of each factor

$\sf \sqrt{b ^{4} } \sqrt{30b}$

Reduce the index of the radical and exponent with 2

$\sf \: {b}^{2} \sqrt{30b}$

Answer 2

$Factor out {b}^{4}$

$\sqrt{30( {b}^{4} b)}$

$Rewrite \: {b}^{4} as {b}^{2} {)}^{2}$

$\sqrt{30(( {b}^{2} {)}^{2} b)}$

$Reorder 30 and {b}^{2} {)}^{2}$

Add parentheses

$\sqrt{( {b}^{2} {)}^{2}.(30b) }$

Pull terms out from under the radical.

${b}^{2} \sqrt{30b}$