a)
[tex] \sqrt{75} = \sqrt{6 {}^{2} \times 2 } = 6 \sqrt{2} [/tex]
b)
[tex] \sqrt{48} = \sqrt{4 {}^{2} \times 3 } = 4 \sqrt{3} [/tex]
c)
[tex] \sqrt{75} = \sqrt{5 {}^{2} \times 3} = 5 \sqrt{3} [/tex]
d)
[tex] \sqrt{90} = \sqrt{3 {}^{2} \times 10 } = 3 \sqrt{10} [/tex]
e)
[tex] \frac{ \sqrt{54} }{ 3} = \frac{3 \sqrt{6} }{3} = \sqrt{6} [/tex]
f)
[tex]5 \sqrt{ \frac{1}{125} } = 5 \times \frac{1}{ \sqrt{125} } = 5 \times \frac{1}{5 \sqrt{5} } = \frac{1}{ \sqrt{5} } = \frac{ \sqrt{5} }{5} [/tex]
g)
[tex] \frac{1}{8} \sqrt{96} = \frac{1}{8} \sqrt{4 {}^{2} \times 6 } = \frac{1}{8} \sqrt{4 {}^{2} } \sqrt{6} = \frac{1}{8} 4 \sqrt{6} = \frac{1}{2} \sqrt{6} = \frac{ \sqrt{6} }{2} [/tex]
h)
[tex] \frac{1}{7} \sqrt{147} = \frac{1}{7} \sqrt{7 {}^{2} \times 3} = \frac{1}{7} \sqrt{7 {}^{2} } \sqrt{3} = \frac{1}{7}7 \sqrt{3} = \sqrt{3} [/tex]
