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

sqrt(48b^(7))=

Simplify. $\newline$ Remove all perfect squares from inside the square root. Assume $\newline$ $b$ is positive. $\newline$ $\sqrt{48b^{7}}$

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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{48b^{7}}

Factor $48$ into primes: First, factor $48$ into its prime factors: $48 = 2^4 \times 3$ .
Separate $b^7$ into perfect squares: Now, separate the $b^7$ into $b^6 \cdot b$ to get perfect squares: $b^7 = b^6 \cdot b$ .
Take out perfect squares from square root: Since $\sqrt{a^2} = a$ , take out the perfect squares from under the square root: $\sqrt{2^4} = 2^2$ and $\sqrt{b^6} = b^3$ .
Multiply numbers outside square root: Now, multiply the numbers outside the square root: $2^2 \times b^3 = 4b^3$ .
Multiply by square root of remaining inside part: Finally, multiply $4b^3$ by the square root of the remaining inside part, which is $\sqrt{3b}$ : $4b^3 \times \sqrt{3b}$ .

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