Question

Question #221ff

Answer 1

`sqrt(72a^19)=6abs(a^9)sqrt(2a)`

Explanation:

To find the square root of the given algebraic expression we
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should find the prime factorization.
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`72=2xx36`
`72=2xx2xx18`
`72=2xx2xx2xx9`
`72=2xx2xx2xx3xx3`
`72=2^3xx3^2`
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`72a^19=2^3xx3^2xx(a^9)^2xxa`
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`sqrt(72a^19)=sqrt(2^3xx3^2xx(a^9)^2xxa)`
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`sqrt(72a^19)=sqrt(2^2xx2xx3^2xx(a^9)^2xxa)`
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`sqrt(72a^19)=sqrt((2xx3xxa^9)^2xx2xxa)`
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`sqrt(72a^19)=abs(2xx3xxa^9)sqrt(2xxa)`
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`sqrt(72a^19)=6abs(a^9)sqrt(2a)`