[simplifying radicals][section 59]
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(1.)  √8                here is the problem
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=    √4√2               factor like this
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=     2√2         take the square root of the 4
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(2.)  √40          here is the problem
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=    √4√10       factor like this
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=    2√10    take the square root of the 4
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(3.)   √20       here is the problem
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=    √4√5         factor like this
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=     2√5   take the square root of the 4
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(4.)  √98           here is the problem
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=    √49*√2           factor like this
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=    7√2      take the square root of the 49
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(5.)   √50          here is the problem
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=   √25√2            factor like this
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=     5√2     take the square root of the 25
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(6.)  √56          here is the problem
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=    √4√14        factor like this
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=     2√14      take the square root of the 4
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(7.)  √24          here is the problem
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=    √4√6              factor like this
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=   2√6         take the square root of the 4
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(8.)  √72          here is the problem
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=   √36√2           factor like this
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=   6√2         take the square root of the 36
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(9.)  √28          here is the problem
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=    √4√7            factor like this
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=    2√7            take the square root of the 4
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(10.)  √35b3              here is the problem
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=     √b2√35b         factor like this
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=     b√35b           cancel
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(11.)  √25m9           here is the problem
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=    √25m8 * √m         factor like this
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=    5m4 √m         take the square root of the 25m8
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(12.)  √32a9b3          here is the problem
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=    √16a8b2 * √2ab        factor like this
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=      4a4b√2ab          take the square root