[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