To simplify the expression [tex]\( 4 \sqrt{96} \times \sqrt{50} \)[/tex], let's go through the steps in detail.
1. Calculate [tex]\( \sqrt{96} \)[/tex]:
The square root of 96 is approximately [tex]\( 9.797958971132712 \)[/tex].
2. Calculate [tex]\( \sqrt{50} \)[/tex]:
The square root of 50 is approximately [tex]\( 7.0710678118654755 \)[/tex].
3. Multiply the square roots:
[tex]\[
\sqrt{96} \times \sqrt{50} \approx 9.797958971132712 \times 7.0710678118654755
\][/tex]
This multiplication gives approximately [tex]\( 69.28203230275508 \)[/tex].
4. Multiply by 4:
[tex]\[
4 \times 69.28203230275508 = 277.12812921102034
\][/tex]
Therefore, the simplified result of the expression [tex]\( 4 \sqrt{96} \times \sqrt{50} \)[/tex] is approximately [tex]\( 277.12812921102034 \)[/tex].
