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Simplify.
Remove all perfect squares from inside the square root. Assume
b is positive.

sqrt(80b^(2))=

Simplify. $\newline$ Remove all perfect squares from inside the square root. Assume $\newline$ $b$ is positive. $\newline$ $\sqrt{80b^{2}} =$

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Simplify radical expressions with variables

Full solution

Q. Simplify.

\newline

Remove all perfect squares from inside the square root. Assume

\newline

b

is positive.

\newline

\sqrt{80b^{2}} =

Factor and express $b^2$ : Factor the number $80$ and express $b^2$ as a perfect square. $\newline$ The number $80$ can be factored into prime factors as $80 = 2 \times 2 \times 2 \times 2 \times 5$ , and since $b$ is positive, $b^2$ is already a perfect square. $\newline$ So, we can write $\sqrt{80b^2}$ as $\sqrt{2^4 \times 5 \times b^2}$ .
Separate perfect squares: Separate the perfect squares from the non-perfect squares inside the square root. $\newline$ We have $\sqrt{2^4 \cdot 5 \cdot b^2}$ which can be written as $\sqrt{2^4}$ $\cdot$ $\sqrt{5}$ $\cdot$ $\sqrt{b^2}$ because the square root of a product is the product of the square roots.
Simplify square roots: Simplify the square roots of the perfect squares. $\newline$ The square root of $2^4$ is $2^2$ , which is $4$ , and the square root of $b^2$ is $b$ . Therefore, we have $4 \cdot \sqrt{5} \cdot b$ .
Combine simplified terms: Combine the simplified terms outside the square root. Multiplying $4$ and $b$ gives us $4b$ . So, the expression simplifies to $4b \times \sqrt{5}$ .
Write final expression: Write the final simplified expression. $\newline$ The final simplified expression is $4b \cdot \sqrt{5}$ .

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