ANSWER
![2 \sqrt{42} +7 \sqrt{2}- 6- \sqrt{21}](https://tex.z-dn.net/?f=2%20%5Csqrt%7B42%7D%20%2B7%20%20%5Csqrt%7B2%7D-%206-%20%5Csqrt%7B21%7D)
EXPLANATION
The given product is:
![( \sqrt{14} - \sqrt{3} )( \sqrt{12} + \sqrt{7} )](https://tex.z-dn.net/?f=%28%20%5Csqrt%7B14%7D%20%20-%20%20%5Csqrt%7B3%7D%20%29%28%20%5Csqrt%7B12%7D%20%2B%20%20%5Csqrt%7B7%7D%20%20%29)
We expand using the distributive property to obtain:
![\sqrt{14}( \sqrt{12} + \sqrt{7}) -\sqrt{3}( \sqrt{12} + \sqrt{7} )](https://tex.z-dn.net/?f=%5Csqrt%7B14%7D%28%20%5Csqrt%7B12%7D%20%2B%20%20%5Csqrt%7B7%7D%29%20-%5Csqrt%7B3%7D%28%20%5Csqrt%7B12%7D%20%2B%20%20%5Csqrt%7B7%7D%20%20%29)
Extract the perfect squares to get:
![\sqrt{14}(2 \sqrt{3} + \sqrt{7}) -\sqrt{3}( 2\sqrt{3} + \sqrt{7} )](https://tex.z-dn.net/?f=%5Csqrt%7B14%7D%282%20%5Csqrt%7B3%7D%20%2B%20%20%5Csqrt%7B7%7D%29%20-%5Csqrt%7B3%7D%28%202%5Csqrt%7B3%7D%20%2B%20%20%5Csqrt%7B7%7D%20%20%29)
Expand further to get;
![2 \sqrt{42} +7 \sqrt{2}- 2(3) - \sqrt{21}](https://tex.z-dn.net/?f=2%20%5Csqrt%7B42%7D%20%2B7%20%20%5Csqrt%7B2%7D-%202%283%29%20%20%20-%20%5Csqrt%7B21%7D%20)
This simplifies to,
![2 \sqrt{42} +7 \sqrt{2}- 6- \sqrt{21}](https://tex.z-dn.net/?f=2%20%5Csqrt%7B42%7D%20%2B7%20%20%5Csqrt%7B2%7D-%206-%20%5Csqrt%7B21%7D%20)
The equivalent to that is 8.
The Answer is 94.2 cubic inches
Answer:
radius of the hemisphere = 9 cm approx
Step-by-step explanation:
Volume of hemisphere = ![\frac{2}{3} \pi r^{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%20r%5E%7B3%7D)
1527.4 = ![\frac{2}{3} * \frac{22}{7} * r^{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%20%2A%20%5Cfrac%7B22%7D%7B7%7D%20%2A%20r%5E%7B3%7D)
= ![r^{3}](https://tex.z-dn.net/?f=r%5E%7B3%7D)
= ![r^{3}](https://tex.z-dn.net/?f=r%5E%7B3%7D)
= 729
r = ![\sqrt[3]{729}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B729%7D)
r = 9 cm approx.
Answer:
q = 18 ?
Step-by-step explanation:
This is not a complete question but ill give it a shot!
If we are following a pattern then we see q is 11 more than r.
So we do 11 + r (7) to get 18!
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