arrange in ascending order: 8 root index blank of 90,fourth root of 10,square root of 6

Asked by nisha_vini29 | 23rd Apr, 2015, 10:58: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space n u m b e r s comma space 8 square root of 90 comma space fourth root of 10 comma square root of 6. L e t space u s space r e w r i t e space t h e space g i v e n space n u m b e r s comma space w i t h o u t space c h a n g i n g space t h e i r space v a l u e s. T h u s comma space 8 square root of 90 equals 8 square root of 9 cross times 10 end root equals 8 cross times 3 square root of 10 equals 24 square root of 10 equals 24 cross times open parentheses 10 close parentheses to the power of 1 half end exponent A n d space space fourth root of 10 equals open parentheses 10 close parentheses to the power of 1 fourth end exponent A l s o comma space square root of 6 equals open parentheses 6 close parentheses to the power of 1 half end exponent T h e r e f o r e comma space t h e space g i v e n space n u m b e r s space a r e colon 24 cross times open parentheses 10 close parentheses to the power of 1 half end exponent comma open parentheses 10 close parentheses to the power of 1 fourth end exponent comma open parentheses 6 close parentheses to the power of 1 half end exponent N o w space c o n s i d e r space t h e space p o w e r s space o f space t h e space g i v e n space n u m b e r s. T h u s comma space L C M space o f space 2 space a n d space 4 space i s space 4. T h u s space w e space c a n space r e w r i t e space t h e space n u m b e r s space a s comma 24 cross times open parentheses 10 close parentheses to the power of 2 over 4 end exponent comma open parentheses 10 close parentheses to the power of 1 fourth end exponent comma open parentheses 6 close parentheses to the power of 2 over 4 end exponent equals 24 cross times open parentheses 10 squared close parentheses to the power of 1 fourth end exponent comma open parentheses 10 close parentheses to the power of 1 fourth end exponent comma open parentheses 6 squared close parentheses to the power of 1 fourth end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 24 cross times open parentheses 100 close parentheses to the power of 1 fourth end exponent comma space open parentheses 10 close parentheses to the power of 1 fourth end exponent comma open parentheses 36 close parentheses to the power of 1 fourth end exponent T h u s comma space t h e space s m a l l e s t space n u m b e r space i n space t h e space s e q u e n c e space i s space open parentheses 10 close parentheses to the power of 1 fourth end exponent. T h u s comma space t h e space n u m b e r s space i n space a s c e n d i n g space o r d e r space i s space open parentheses 10 close parentheses to the power of 1 fourth end exponent comma space open parentheses 36 close parentheses to the power of 1 fourth end exponent comma space 24 cross times open parentheses 10 squared close parentheses to the power of 1 fourth end exponent

Answered by Vimala Ramamurthy | 24th Apr, 2015, 10:17: AM