Question

solve this with explanation .please .​

Answer 1

Answer:

$= 2^{ \frac{3}{2} }$

Step-by-step explanation:

$= \sqrt{2 \times \sqrt{2 \times \sqrt{2} } }$

$= {2}^{ \frac{1}{2} } \times 2 ^{ \frac{1}{2} } \times 2^{ \frac{1}{2} }$

$= 2 ^{ \frac{1 + 1 + 1}{2 } }$

$= 2 ^{ \frac{3}{2} }$

Answer 2

Answer:

2⅞

Step-by-step explanation:

$\sqrt{2 \sqrt{2 \times 2 \frac{1}{2} } }$

$\sqrt{2 \sqrt{2 {}^{1 + 1 \div 2} } }$

$\sqrt{2 \sqrt{2 {}^{3 \div 2} } }$

$\sqrt{2 \times 2 {}^{3 \div 2 \times 1 \div 2} }$

$\sqrt{2 {}^{1 + 3 \div 4} }$

$\sqrt{2 {}^{7 \div 4} }$

$2 {}^{7 \div 4 \times 1 \div 2}$

$2 {}^{7 \div 8}$