Question

. Use the process outlined in the lesson to approximate the number 3√10. Use the approximation √10 ≈3162 277 7.

Answer 1

Answer:

sequence of five intervals

(1) 3³  < $3^{\sqrt{10} }$   < $3^{4}$

(2) $3^{3.1}$  < $3^{\sqrt{10} }$   < $3^{3.2}$

(3) $3^{3.16}$ < $3^{\sqrt{10} }$   < $3^{3.17}$

(4) $3^{3.162}$ < $3^{\sqrt{10} }$   < $3^{3.163}$

(5) $3^{3.1622}$  < $3^{\sqrt{10} }$   < $3^{3.1623}$

Step-by-step explanation:

as per question given data      

√10 ≈ 3.162 277 7    

to find out      

sequence of five intervals

solution      

as we have given that √10 value that is here

√10 ≈ 3.162 277 7           ........................1

so  

when we find $3^{\sqrt{10} }$           ................2

put here √10 value in equation number  2  

we get  $3^{\sqrt{10} }$   that is  32.27    

so    

sequence of five intervals

(1) 3³  < $3^{\sqrt{10} }$   < $3^{4}$

(2) $3^{3.1}$  < $3^{\sqrt{10} }$   < $3^{3.2}$

(3) $3^{3.16}$ < $3^{\sqrt{10} }$   < $3^{3.17}$

(4) $3^{3.162}$ < $3^{\sqrt{10} }$   < $3^{3.163}$

(5) $3^{3.1622}$  < $3^{\sqrt{10} }$   < $3^{3.1623}$