# 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))

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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Kaeden Lara
1) $3\sqrt{75}=3\sqrt{\left[\left(25\right)\ast 3\right]}=5\ast 3\sqrt{3}=5\sqrt{\left[\left(3\right)2\ast \left(3\right)\right]}=5\sqrt{\left(9\ast 3\right)}=5\sqrt{27}$ TRUE
2) 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 $\left(3/2{\right)}^{1/2}>\left(2/3{\right)}^{1/2}$ so that $3\left(3/2{\right)}^{1/2}>3\left(2/3{\right)}^{1/2}>2\left(2/3{\right)}^{1/2}$ . Hemce the statement is FALSE