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Simplify.
Remove all perfect squares from inside the square root.

sqrt(30b^(5))=

Simplify. $\newline$ Remove all perfect squares from inside the square root. $\newline$ $\sqrt{30b^{5}}$

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Simplify radical expressions with variables

Full solution

Q. Simplify.

\newline

Remove all perfect squares from inside the square root.

\newline

\sqrt{30b^{5}}

Factor the expression: Factor the expression inside the square root to identify perfect squares. $\newline$ We need to factor $30b^5$ into its prime factors and identify any perfect squares. $\newline$ $30b^5 = 2 \times 3 \times 5 \times b^4 \times b$ $\newline$ Here, $b^4$ is a perfect square because $(b^2)^2 = b^4$ .
Rewrite with perfect square: Rewrite the square root with the perfect square separated. $\newline$ Now we can rewrite $\sqrt{30b^5}$ as $\sqrt{2 \cdot 3 \cdot 5 \cdot b^4 \cdot b}$ , which is the same as $\sqrt{b^4}$ $\cdot$ $\sqrt{2 \cdot 3 \cdot 5 \cdot b}$ .
Simplify perfect square: Simplify the square root of the perfect square. $\newline$ Since $\sqrt{b^4}$ is the square root of a perfect square, it simplifies to $b^2$ . $\newline$ So we have $b^2 \cdot \sqrt{2 \cdot 3 \cdot 5 \cdot b}$ .
Combine and simplify: Combine the constants under the square root and simplify. $\newline$ We have $b^2 \sqrt{2 \cdot 3 \cdot 5 \cdot b}$ which simplifies to $b^2 \sqrt{30b}$ .

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