Question

Given that sqrt40 = k sqrt10 Find the value of k and please explain

$\begin{array}{rcll} \sqrt{40 } &=& k\cdot \sqrt{10} & \qquad |\qquad \text{square both sides} \\ (\sqrt{40 })^2 &=& (k\cdot \sqrt{10})^2 \\ 40 &=& k^2\cdot 10 & \qquad |\qquad :10 \\ \frac{40}{10} &=& k^2 & \\ 4 &=& k^2 & \\ k^2 &=& 4 &\qquad |\qquad \sqrt{()} \text{ both sides} \\ \sqrt{ k^2 } &=& \sqrt{4} & \\ \mathbf{k} & \mathbf{=} & \mathbf{2}& \\ \end{array}$

Given that sqrt40 = k sqrt10 Find the value of k and please explain

k=sqrt(40)/sqrt(10, but 40=2 X 2 X 10=2sqrt(10), so we have:

k=2sqrt(10)/sqrt(10), sqrt(10) cancels out, so we have:

k=2