29.
a)
[tex] \sqrt{ {6}^{3} \times 6 } = \sqrt{ {6}^{4} } = {6}^{2} = 36[/tex]
b)
[tex] \sqrt{ {11}^{4} \times 9 } = \sqrt{ {11}^{4} \times {3}^{2} } = [/tex]
[tex] = {11}^{2} \times 3 = 121 \times 3 = 363[/tex]
c)
[tex] \sqrt{ {2}^{6} \times {3}^{4} \times 25} = \sqrt{ {2}^{6} \times {3}^{4} \times {5}^{2} } = [/tex]
[tex] = {2}^{3} \times {3}^{2} \times 5 = 8 \times 9 \times 5 = [/tex]
=360
d)
[tex] \sqrt{196 \times {2}^{6} \times 81} = [/tex]
[tex] = \sqrt{ {14}^{2} \times {2}^{6} \times {9}^{2} } = [/tex]
[tex] = 14 \times {2}^{3} \times 9 = [/tex]
=14×8×9=1008
e)
[tex] \sqrt{ {15}^{2} - {9}^{2} \ + {5}^{2} } = [/tex]
[tex] = \sqrt{225 - 81 + 25} = [/tex]
[tex] \sqrt{169} = 13[/tex]
f)
[tex] \sqrt{ {72}^{2} - {71}^{2} + {5}^{2} + 1} = [/tex]
[tex] = \sqrt{5184 - 5041 + 25 + 1} = [/tex]
[tex] = \sqrt{143 + 25 + 1} = [/tex]
[tex] = \sqrt{169} = 13[/tex]
g)
[tex] \sqrt{7 \times ( {12}^{2} - {9}^{2} )} = [/tex]
[tex] = \sqrt{7 \times (144 - 81)} = [/tex]
[tex] = \sqrt{7 \times 63} = \sqrt{ {7}^{2} \times {9}^{2} } = [/tex]
[tex] = 7 \times 3 = 21[/tex]
h)
[tex] \sqrt{ {2}^{8} ( {7}^{2} - {2}^{4} \times 3)} = [/tex]
[tex] \sqrt{ {2}^{8} \times (49 - 48) } = [/tex]
[tex] \sqrt{ {2}^{8} \times 1 } = \sqrt{ {2}^{8} } = {2}^{4} = 16[/tex]
