Solve the following equation: $$ \sqrt{15}=\sqrt{6 \mathrm{k}-14} $$ Provide an answer accurate to the nearest hundredth.

Question

UpStudy AI · Accepted Answer

To solve the equation

$$
\sqrt{15} = \sqrt{6k - 14},
$$

we start by squaring both sides to eliminate the square roots:

$$
15 = 6k - 14.
$$

Next, we isolate $$6k$$ by adding 14 to both sides:

$$
15 + 14 = 6k,
$$

which simplifies to

$$
29 = 6k.
$$

Now, we solve for $$k$$ by dividing both sides by 6:

$$
k = \frac{29}{6}.
$$

To express this as a decimal, we perform the division:

$$
k \approx 4.8333\ldots.
$$

Rounding this to the nearest hundredth, we find:

$$
k \approx 4.83.
$$

Thus, the solution to the equation is

$$
\boxed{4.83}.
$$
The solution to the equation is $$ k \approx 4.83 $$.

Solve the following equation: \[ \sqrt{15}=\sqrt{6 \mathrm{k}-14} \] Provide an answer accurate to the nearest hundredth.