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goldfiish [28.3K]
3 years ago
14

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

Mathematics
1 answer:
GaryK [48]3 years ago
5 0

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}

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