Simplify. Remove all perfect squares from inside the square roots. Assume a and b are positive. sqrt(81a^(5)b)=

Identify perfect squares: Identify the perfect squares in the expression sqrt(81a^(5)b). The number 81 is a perfect square because 81 = 9^2. The term a^(5) can be broken down into a^(4)*a, where a^(4) is a perfect square because (a^2)^2 = a^(4). The term b does not have a perfect square since it is to the first power.Separate perfect squares: Rewrite the expression by separating the perfect squares from the non-perfect squares. sqrt(81a^(5)b) = sqrt(9^2 * a^(4) * a * b)Simplify perfect squares: Simplify the square root of the perfect squares. Since the square root of a perfect square is the base of the square, we have: sqrt(9^2 * a^(4) * a * b) = 9 * a^2 * sqrt(a * b)Write final simplified expression: Write the final simplified expression. The final simplified expression is 9a^2 * sqrt(ab).

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Simplify.
Remove all perfect squares from inside the square roots. Assume
a and
b are positive.

sqrt(81a^(5)b)=

Simplify. $\newline$ Remove all perfect squares from inside the square roots. Assume $\newline$ $a$ and $\newline$ $b$ are positive. $\newline$ $\sqrt{81a^{5}b}$ =

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Math Problems

Algebra 1

Simplify radical expressions with variables

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Q. Simplify.

\newline

Remove all perfect squares from inside the square roots. Assume

\newline

a

and

\newline

b

are positive.

\newline

\sqrt{81a^{5}b}

Identify perfect squares: Identify the perfect squares in the expression $\sqrt{81a^{5}b}$ . $\newline$ The number $81$ is a perfect square because $81 = 9^2$ . The term $a^{5}$ can be broken down into $a^{4} \cdot a$ , where $a^{4}$ is a perfect square because $(a^2)^2 = a^{4}$ . The term $b$ does not have a perfect square since it is to the first power.
Separate perfect squares: Rewrite the expression by separating the perfect squares from the non-perfect squares. $\newline$ $\sqrt{81a^{5}b} = \sqrt{9^2 \cdot a^{4} \cdot a \cdot b}$
Simplify perfect squares: Simplify the square root of the perfect squares. $\newline$ Since the square root of a perfect square is the base of the square, we have: $\newline$ $\sqrt{9^2 \cdot a^{4} \cdot a \cdot b} = 9 \cdot a^2 \cdot \sqrt{a \cdot b}$
Write final simplified expression: Write the final simplified expression. $\newline$ The final simplified expression is $9a^2 \cdot \sqrt{ab}$ .