True or false? Give your reasoning either way. 1. 5 sqrt(27) = 3 sqrt{75} 2. sqrt(8) + sqrt(32) = sqrt(40) 3. 2 sqrt((2)/(3)) = 3 sqrt((3)/(2))

Brenda Jordan 2022-11-17 Answered
True or false? Give your reasoning either way.
1. 5 \sqrt{27} = 3 \sqrt{75}
2. \sqrt{8} + \sqrt{32} = \sqrt{40}
3. 2 \sqrt{\frac{2}{3}} = 3 \sqrt{\frac{3}{2}}
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Answers (1)

Kaeden Lara
Answered 2022-11-18 Author has 23 answers
1) 3 75 = 3 [ ( 25 ) 3 ] = 5 3 3 = 5 [ ( 3 ) 2 ( 3 ) ] = 5 ( 9 3 ) = 5 27 TRUE
2) 8 + 32 = 2 2 + 4 2 = 6 2 (   a s   8 = ( 2 ) 2 2   a n d   32 = ( 4 ) 2 2   A l s o   40 = [ ( 2 ) 2 2 5 ] = 2 ( 2 ) ( 5 ) FALSE
3) FALSE The statement is apparently false on 1st scrutiny itself . 3/2 is 1.5 and 2/3 is 0.6666666666......
Therefore 3/2 > 2/3 so that ( 3 / 2 ) 1 / 2 > ( 2 / 3 ) 1 / 2 so that 3 ( 3 / 2 ) 1 / 2 > 3 ( 2 / 3 ) 1 / 2 > 2 ( 2 / 3 ) 1 / 2 . Hemce the statement is FALSE
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