$$sqrt\dfrac{40x^5}{s}qrt\cdot5x^2=\dfrac{200q^2r^2st^2x^7}{s}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}sqrt\frac{40x^5}{s}qrt\cdot5x^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{40qrstx^5}{s}qrt\cdot5x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{40q^2rstx^5}{s}rt\cdot5x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{40q^2r^2stx^5}{s}t\cdot5x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{40q^2r^2st^2x^5}{s}\cdot5x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{200q^2r^2st^2x^7}{s}\end{aligned} $$ | |
| ① | Multiply $qrst$ by $ \dfrac{40x^5}{s} $ to get $ \dfrac{ 40qrstx^5 }{ s } $. Step 1: Write $ qrst $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} qrst \cdot \frac{40x^5}{s} & \xlongequal{\text{Step 1}} \frac{qrst}{\color{red}{1}} \cdot \frac{40x^5}{s} \xlongequal{\text{Step 2}} \frac{ qrst \cdot 40x^5 }{ 1 \cdot s } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 40qrstx^5 }{ s } \end{aligned} $$ |
| ② | Multiply $ \dfrac{40qrstx^5}{s} $ by $ q $ to get $ \dfrac{ 40q^2rstx^5 }{ s } $. Step 1: Write $ q $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{40qrstx^5}{s} \cdot q & \xlongequal{\text{Step 1}} \frac{40qrstx^5}{s} \cdot \frac{q}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 40qrstx^5 \cdot q }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 40q^2rstx^5 }{ s } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{40q^2rstx^5}{s} $ by $ r $ to get $ \dfrac{ 40q^2r^2stx^5 }{ s } $. Step 1: Write $ r $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{40q^2rstx^5}{s} \cdot r & \xlongequal{\text{Step 1}} \frac{40q^2rstx^5}{s} \cdot \frac{r}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 40q^2rstx^5 \cdot r }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 40q^2r^2stx^5 }{ s } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{40q^2r^2stx^5}{s} $ by $ t $ to get $ \dfrac{ 40q^2r^2st^2x^5 }{ s } $. Step 1: Write $ t $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{40q^2r^2stx^5}{s} \cdot t & \xlongequal{\text{Step 1}} \frac{40q^2r^2stx^5}{s} \cdot \frac{t}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 40q^2r^2stx^5 \cdot t }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 40q^2r^2st^2x^5 }{ s } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{40q^2r^2st^2x^5}{s} $ by $ 5x^2 $ to get $ \dfrac{ 200q^2r^2st^2x^7 }{ s } $. Step 1: Write $ 5x^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{40q^2r^2st^2x^5}{s} \cdot 5x^2 & \xlongequal{\text{Step 1}} \frac{40q^2r^2st^2x^5}{s} \cdot \frac{5x^2}{\color{red}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 40q^2r^2st^2x^5 \cdot 5x^2 }{ s \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 200q^2r^2st^2x^7 }{ s } \end{aligned} $$ |