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Find the square root of (2x^(2)-7x-15)(2...

Find the square root of `(2x^(2)-7x-15)(2x^(2)-24x+70)(2x^(2)-11x-21)`.

Text Solution

Verified by Experts

First of all we shall factorise each expression of given product separately.
`2x^(2)-7x-15=2x^(2)-10x+3x-15`
`=2x(x-5)+3(x-5)`
`=(x-5)(2x+3)`
`2x^(2)-24x+70=2(x^(2)-12x+35)`
`=2(x^(2)-5x-7x+35)=2[x(x-5)-7(x-5)]`
`=2(x-5)(x-7)
`2x^(2)-11x-21=2x^(2)-14x+3x-21`
=2x(x-7)+3(x-7)=(x-7)(2x+3)`
`therefore` Given product is
`(x-5)(2x+3).2(x-5)(x-7)(2x+3)`
`=2(x-5)^(2)(x-7)^(2)(2x+3)^(2)`

`therefore` Its square root is
`sqrt(2(x-5)^(2)(x-7)^(2)(2x+3)^(2))`
`=sqrt(2)(x-5)(x-7)(2x+3)`
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