Certainly! Let's solve the problem step-by-step.
We are asked to divide [tex]\( 8 \sqrt{15} \)[/tex] by [tex]\( 2 \sqrt{3} \)[/tex].
Step 1: Write the expression as a fraction
[tex]\[
\frac{8 \sqrt{15}}{2 \sqrt{3}}
\][/tex]
Step 2: Simplify the coefficients
Simplify the fraction by dividing the coefficients (numbers outside the square roots):
[tex]\[
\frac{8}{2} = 4
\][/tex]
This reduces our expression to:
[tex]\[
4 \frac{\sqrt{15}}{\sqrt{3}}
\][/tex]
Step 3: Simplify the radicals
We know from the properties of square roots that:
[tex]\[
\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}
\][/tex]
Apply this to our expression:
[tex]\[
\frac{\sqrt{15}}{\sqrt{3}} = \sqrt{\frac{15}{3}} = \sqrt{5}
\][/tex]
Step 4: Combine the simplified expressions
So, the expression now is:
[tex]\[
4 \sqrt{5}
\][/tex]
Step 5: Calculate the numerical values
Finally, if we need the numerical values:
- The original values were approximately [tex]\( 8 \sqrt{15} \approx 30.98387 \)[/tex] and [tex]\( 2 \sqrt{3} \approx 3.46410 \)[/tex]
- Performing the division, [tex]\( 30.98387 / 3.46410 \approx 8.94427 \)[/tex]
- Therefore, the simplified result [tex]\( 4 \sqrt{5} \approx 8.94427 \)[/tex]
To sum up, our simplified result is:
[tex]\[
4 \sqrt{5} \approx 8.94427
\][/tex]
This is the step-by-step breakdown for dividing [tex]\( 8 \sqrt{15} \)[/tex] by [tex]\( 2 \sqrt{3} \)[/tex].
