Question

4. Use the process outlined in the lesson to approximate the number 2√3. Use the approximation √3 ≈ 1.732 050 8.

Answer 1

Answer:

sequence of five intervals

(1) 2  < $2^{\sqrt{3} }$   < $2^{2}$

(2) $2^{1.7}$  < $2^{\sqrt{3} }$    < $2^{1.8}$

(3) $2^{1.73}$  < $2^{\sqrt{3} }$    < $2^{1.74}$

(4) $2^{1.732}$  < $2^{\sqrt{3} }$    < $2^{1.733}$

(5) $2^{1.7320}$  < $2^{\sqrt{3} }$    < $2^{1.7321}$

Step-by-step explanation:

as per question given data      

√3 ≈ 1.732 050 8 

to find out      

sequence of five intervals

solution      

as we have given that √3 value that is here

√3 ≈ 1.732 050 8            ........................1

so  

when we find $2^{\sqrt{3} }$           ................2

put here √3 value in equation number  2  

we get  $2^{\sqrt{3} }$   that is  3.322    

so    

sequence of five intervals

(1) 2  < $2^{\sqrt{3} }$   < $2^{2}$

(2) $2^{1.7}$  < $2^{\sqrt{3} }$    < $2^{1.8}$

(3) $2^{1.73}$  < $2^{\sqrt{3} }$    < $2^{1.74}$

(4) $2^{1.732}$  < $2^{\sqrt{3} }$    < $2^{1.733}$

(5) $2^{1.7320}$  < $2^{\sqrt{3} }$    < $2^{1.7321}$