8sqrtp-2sqrt3=sqrt3+3sqrtp What value of p is the solution to the given equation? Choose 1 answer: (A) (3sqrt3)/(5) (B) (9)/(5) (c) (9)/(25) (C) (27)/(25)

Isolate terms involving p: First, let's isolate the terms involving $ p $ on one side and the constants on the other side of the equation. We start by moving all terms involving $ \sqrt{p} $ to the left and all constant terms to the right: \[ 8\sqrt{p} - 3\sqrt{p} = \sqrt{3} + 2\sqrt{3} \]Simplify both sides: Simplify both sides: \[ 5\sqrt{p} = 3\sqrt{3} \] Now, to eliminate the square root, square both sides of the equation: \[ (5\sqrt{p})^2 = (3\sqrt{3})^2 \]Eliminate square root: Perform the squaring: \[ 25p = 27 \] Next, solve for $ p $ by dividing both sides by 25: \[ p = \frac{27}{25} \]

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$8\sqrt{p}-2\sqrt{3}=\sqrt{3}+3\sqrt{p}$ $\newline$ What value of $p$ is the solution to the given equation? $\newline$ Choose $1$ answer: $\newline$ (A) $(3\sqrt{3})/(5)$ $\newline$ (B) $(9)/(5)$ $\newline$ (C) $(9)/(25)$ $\newline$ (D) $(27)/(25)$

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Algebra 2

Simplify rational expressions

Full solution

8\sqrt{p}-2\sqrt{3}=\sqrt{3}+3\sqrt{p}

\newline

What value of

p

is the solution to the given equation?

\newline

Choose

1

answer:

\newline

(A)

(3\sqrt{3})/(5)

\newline

(B)

(9)/(5)

\newline

(C)

(9)/(25)

\newline

(D)

(27)/(25)

Isolate terms involving p: First, let's isolate the terms involving $p$ on one side and the constants on the other side of the equation. We start by moving all terms involving $\sqrt{p}$ to the left and all constant terms to the right: $\newline$ $8\sqrt{p} - 3\sqrt{p} = \sqrt{3} + 2\sqrt{3}$
Simplify both sides: Simplify both sides: $\newline$ $5\sqrt{p} = 3\sqrt{3}$ $\newline$ Now, to eliminate the square root, square both sides of the equation: $\newline$ $(5\sqrt{p})^2 = (3\sqrt{3})^2$
Eliminate square root: Perform the squaring: $\newline$ $25p = 27$ $\newline$ Next, solve for $p$ by dividing both sides by $25$ : $\newline$ $p = \frac{27}{25}$