Question

$\sqrt{(2^2)^2+2(2^{-1})+((2^{10})^{\frac{1}{2}})}$ = 

• A. 6
• B. $\sqrt20$
• C. $\sqrt48$
• D. 7

Answer 1

Answer:

D. 7

The value of the expression is 7.

We simplify each term inside the square root one by one:

1. Simplify the first term:
$(2^2)^2 = 2^{2 \times 2} = 2^4 = 16$

2. Simplify the second term:
$2(2^{-1}) = 2^1 \times 2^{-1} = 2^{1-1} = 2^0 = 1$

3. Simplify the third term:
$((2^{10})^{\frac{1}{2}}) = 2^{10 \times \frac{1}{2}} = 2^5 = 32$

4. Add the terms together inside the square root:
$\sqrt{16 + 1 + 32} = \sqrt{49}$

5. Find the square root:
$\sqrt{49} = 7$