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यदि `sqrt(5)=2.236` व `sqrt(10)=3.162`, तब `(15)/(sqrt(10)+sqrt(20)+sqrt(40)-sqrt(5)-sqrt(80))` का मान ज्ञात कीजिए । |
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Answer» यहाँ `sqrt(10)+sqrt(20)+sqrt(40)-sqrt(5)-sqrt(80)` `=sqrt(10)+sqrt(2^(2)xx5)+sqrt(2^(2)xx10)-sqrt(5)-sqrt(2^(4)xx5)` `=sqrt(10)+2sqrt(5)+2sqrt(10)-sqrt(5)-4sqrt(5)=sqrt(10)+2sqrt(10)+2sqrt(5)-sqrT(5)-4sqrt(5)` `=(1+2)sqrt(10)+(2-1-4)sqrt(5)=3(sqrt(10)-sqrt(5))` अतः `(15)/(sqrt(10)+sqrt(20)+sqrt(40)-sqrt(5)-sqrt(80))` `=(15)/(3(sqrt(10)-sqrt(5)))=(5)/(sqrt(10)-sqrT(5))=(5(sqrt(10)+sqrt(5)))/((sqrt(10)-sqrt(5))(sqrt(10)+sqrt(5)))` `=(5(sqrt(10)+sqrt(5)))/(10-5)=sqrt(10)+sqrt(5)=3.162+2.236=5.398` |
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